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7th Grade

2D Geometry

2015-11-19

www.njctl.org

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Table of Contents

Click on a topic to go to that sectionSpecial Pairs of Angles

Perimeter & CircumferenceArea of Rectangles

Area of Irregular Figures Area of Shaded Regions

Area of ParallelogramsArea of TrianglesArea of TrapezoidsArea of CirclesMixed Review

Glossary

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Special Pairsof Angles

Return to Table of Contents

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Angle

A

B C1

side

sidevertex

An angle has three parts, it has two sides (the rays that make the

angle) and one vertex, where the sides meet.

In this example, the sides are the rays BA and BC

and the vertex is B.

An angle is the intersection of 2 rays with a common endpoint.

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Naming Angles

A

B C1

side

sidevertex

· By its vertex (B in the figure shown)

· By a point on one side, its vertex and a point on the other side (either ABC or CBA in the figure shown)

· Or by a letter or number placed inside the angle (1 in the figure)

An angle can be named in three different ways:

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Congruent Angles have the same angle measurement.

Congruent Angles

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1 Are the two angles congruent?

Yes

No

75o110o

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2 Are the two angles congruent angles?

Yes

No

40o

40o

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3 Are the two angles congruent?

Yes

No

75o105o

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Complementary Angles are two angles with a sum of 90 degrees.

These two angles are complementary angles because their sum is 90.

Notice that they form a right angle when placed together.

Complementary Angles

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Complementary Angles are two angles with a sum of 90 degrees.

These two angles are complementary angles because their sum is 90.

Although they aren't placed together, they can still be complementary.

Complementary Angles

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4

What is the measure of ∠1?

50°

1

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5

What is the measure of ∠2?

57

57°2

57575757

57 57

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6 Tell whether the two angles are complementary?

Yes

No

m∠3 = 63°m∠4 = 27°

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7 Tell whether the angles are complementary.

Yes

No

m∠5 = 146°m∠6 = 44°

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Supplementary Angles are two angles with a sum of 180 degrees.

These two angles are supplementary angles because their sum is 180.

Notice that they form a straight angle when placed together.

Supplementary Angles

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Supplementary Angles are two angles with a sum of 180 degrees.

These two angles are supplementary angles because their sum is 180.

Although they aren't placed together, they can still be supplementary.

Supplementary Angles

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8 What is the measurement of angle 1?

Angle 1125°

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9 What is the measurement of angle 2?

Angle 2 40°

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10 Tell whether the two angles are supplementary.

Yes

No

m∠3 = 115°m∠4 = 65°

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11 Find the supplement of 51°.

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12 Find the complement of 51°.

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13 Find the complement of 27°.

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14 Find the supplement of 27°.

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15 Find the supplement of 102°.

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16 Find the complement of 102°.

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Vertical Angles are two angles that are opposite each other when two lines intersect.

12

34

In this example, the vertical angles are:

Vertical angles have the same measurement. So:

∠1 & ∠3∠2 & ∠4

m∠1 = m∠3m∠2 = m∠4

Vertical Angles

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m∠2 = 35° m∠1 = 180 - 35m∠1 = 135°

m∠3 = 180 - 35m∠3 = 135°

23

135°

Using what you know about complementary, supplementary and vertical angles, find the measure of each missing angle.

Click Click

By Vertical Angles: By Supplementary Angles:

Missing Angles

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17 Are angles 2 and 4 vertical angles?

YesNo

12

34

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18 Are angles 2 and 3 vertical angles?

YesNo

12

34

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19 If angle 1 is 60 degrees, what is the measure of angle 3? You must be able to explain why.

21 3

4

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20 If angle 1 is 60 degrees, what is the measure of angle 2? You must be able to explain why.

21 3

4

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Adjacent Angles are two angles that are next to each other and have a common ray between them. This means that they are on the same plane and they share no internal points.

A

B

C

D

is adjacent to

How do you know?· They have a common side (ray )· They have a common vertex (point B)

Adjacent Angles

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Adjacent or Not Adjacent? You Decide!

a

b ab

a

b

Adjacent Not Adjacent Not Adjacentclick click click

Adjacent Angles

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21 Which two angles are adjacent to each other?

A 1 and 4B 2 and 4

1

23

456

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22 Which two angles are adjacent to each other?

A 3 and 6B 5 and 4

12

34 5

6

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Interactive Activity-Click Here

A

PQ

RB

A

E

F

A transversal is a line that cuts across two or more (usually parallel) lines.

Transveral

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Corresponding Angles are on the same side of the transversal and in the same location at each intersection.

1 2

3 4

5 6

7 8

Tran

sver

sal

In this diagram the corresponding angles are:

∠1 & ∠5∠2 & ∠6∠3 & ∠7∠4 & ∠8

Corresponding Angles

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23 Which are pairs of corresponding angles?

A 2 and 6B 3 and 7C 1 and 8

1 2

3 4

5 6

7 8

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24 Which are pairs of corresponding angles?

A 2 and 6B 3 and 1C 1 and 8

1

23

4

56

78

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25 Which are pairs of corresponding angles?

A 1 and 5B 2 and 8C 4 and 8

1 2

3 4

56

7 8

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26 Which pair of angles are not corresponding?

ABCDE

1

2

3

45

6

7

8

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Alternate Exterior Angles are on opposite sides of the transversal and on the outside of the given lines.

m

n

k

1 2

3 4

5 6

7 8

In this diagram the alternate exterior angles are:

Which line is the transversal?

∠1 & ∠8∠2 & ∠7

Alternate Exterior Angles

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Alternate Interior Angles are on opposite sides of the transversal and on the inside of the given lines.

In this diagram the alternate interior angles are: m

n

k

1 2

3 4

5 6

7 8

∠3 & ∠6∠4 & ∠5

Alternate Interior Angles

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Same Side Interior Angles are on same sides of the transversal and on the inside of the given lines.

In this diagram the same side interior angles are:

m

n

k

1 2

3 4

5 6

7 8

∠3 & ∠5∠4 & ∠6

Same Side Interior Angles

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27 Are angles 2 and 7 alternate exterior angles?

YesNo

1 35 7

2 46 8

m

n

l

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28 Are angles 3 and 6 alternate exterior angles?

YesNo

1 35 7

2 46 8

m

n

l

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29 Are angles 7 and 4 alternate exterior angles?

YesNo

1 35 7

2 46 8

m

n

l

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30 Which angle corresponds to angle 5?

ABCD

1 35 7

2 46 8

m

n

l

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31 Which pair of angles are same side interior?

ABCD

1 35 7

2 46 8

m

n

l

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32

What type of angles are ∠3 and ∠6?

A Alternate Interior Angles B Alternate Exterior Angles C Corresponding Angles D Vertical Angles 1 3

5 7

2 4

8

m

n

l

6

E Same Side Interior

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33

What type of angles are ∠5 and ∠2?

A Alternate Interior Angles B Alternate Exterior Angles C Corresponding Angles D Vertical Angles

1 35 7

2 68 4

m

n

l

E Same Side Interior

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34

What type of angles are ∠5 and ∠6?

A Alternate Interior Angles B Alternate Exterior Angles C Corresponding Angles D Vertical Angles E Same Side Interior

4

8

2

6

3

7

1

5

m

n

l

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35 Are angles 5 and 2 alternate interior angles?

YesNo

1 32 4

5 67 8

m

n

l

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36 Are angles 5 and 7 alternate interior angles?

YesNo

13

57

24

68

mn

l

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37 Are angles 7 and 2 alternate interior angles?

YesNo

1 53 7

2 64 8

m

n

l

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38 Are angles 3 and 6 alternate exterior angles?

YesNo

1 23 4

5 76 8

m

n

l

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If parallel lines are cut by a transversal then:

· Corresponding Angles are congruent· Alternate Interior Angles are congruent· Alternate Exterior Angles are congruent

So:1 3

5 7

2 46 8

l

m

n

Special Case

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39 Given the measure of one angle, find the measures of as many angles as possible. Which angles are congruent to the given angle? Type one of them into your responder.

4 5

6

2 71 8

l

m

n

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40 Given the measure of one angle, find the measures of as many angles as possible. What are the measures of the remaining angles?

4 5

6

2 71 8

l

m

n

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41 Given the measure of one angle, find the measures of as many angles as possible. Which angles are congruent to the given angle? Type one of them into your responder.

1 3

5 7

2 48

m

n

l

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42 Given the measure of one angle, find the measures of as many angles as possible. What are the measures of the remaining angles?

13

5

7

24

8

mn

l

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Perimeter & Circumference

Return to Table of Contents

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Perimeter

Perimeter: The distance around a two-dimensional figure.

ww

l

l

Note: ( l) represents the Length, or longer side of the rectangle. ( w) represents the Width, or shorter side of the rectangle. If no units are given, use " u".

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Perimeter (P) of a rectangle is found by using the following formula:

P = 2l + 2w

Perimeter (P) of a square is found by doing four (4) times Side ( s):

P = 4ss

Perimeter of a polygon is the sum of the lengths of the sides.

Perimeter

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43 What is the Perimeter (P) of the following rectangle?

15 ft.

6 ft.

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44 What is the Perimeter (P) of the square below?

7

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45 What is the Perimeter (P) of the figure?

8 in

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46 What is the Perimeter (P) of the figure?

10 cm

12 cm

8 cm

3 cm

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Circumference

Circumference: The outer boundary of a circle; the "perimeter" of the circle.

Circumference

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The circumference (C) of a circle is found by using one of the following formulas:

C = dor

C = 2ror

C = 2 r

Circumference

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Diameter (d): Any straight line segment that passes through the center of the circle, whose endpoints are on the circle.

C = dor

C = 2 r

Circumference

Radius (r): Any line segment from the center of the circle, to any point on the circle - Note: the radius is 1/2 of the diameter.

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Pi ( ): a mathematical constant, is the ratio of a circle's circumference to its diameter.

Note:

C = dor

C = 2 r

Circumference

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47 What is the Circumference (C) of a circle with a radius (r) of 7 cm? (Use 3.14 for # )

7 cm

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48 What is the Circumference (C) of a circle with a Diameter (D) of 11 in.? (Use 3.14 for # )

11 in.

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49 Find the circumference of a circle whose radius is 2.5 meters. (Use 3.14 for # )

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50 A circle has diameter 8 yds. What is its circumference? (Use 3.14 for # )

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51 The circumference of a circle is 37.68 cm. What is its radius? (Use 3.14 for # )

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Sometimes, a question will ask you to "Leave your answer in terms of π". This means that you treat π like a variable & only do the arithmetic operations with the remaining numbers.

Ex: If a circle has a radius of 4, then

Circumference = 2π(4)

= 8π units

Let's try some more problems like this one.

Click here to return to Area of a Circle.

Answer in Terms of π

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9 cm

Find the Circumference. Leave your answer in terms of π.

Answer in Terms of π

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Find the Circumference. Leave your answer in terms of π.

15 in.

Answer in Terms of π

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52 What is the Circumference (C) of a circle with a radius (r) of 7 cm? Leave your answer in terms of π.

7 cm

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53 What is the Circumference (C) of a circle with a Diameter (D) of 11 in.? Leave your answer in terms of π.

11 in.

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54 Find the circumference of a circle whose radius is 2.5 meters. Leave your answer in terms of π.

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55 A circle has diameter 8 yds. What is its circumference? Leave your answer in terms of π.

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56 The circumference of a circle is 19 π cm. What is its radius?

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Area of Rectangles

Return to Table of Contents

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Area - The number of square units (units2) it takes to cover the surface of a figure.

ALWAYS label units2!!!

12 ft

6 ft

Area

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How many 1 ft 2 tiles does it take to cover the rectangle?

Use the squares to find out!

Look for a faster way than covering the whole figure.

12 ft

6 ft

Area

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A = length(width)A = lw

A = side(side)A = s2

The Area (A) of a rectangle is found by using the formula:

The Area (A) of a square is found by using the formula:

Area

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57 What is the Area (A) of the figure?

15 ft

6 ft

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58 Find the area of the figure below.

7 units

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Area of Parallelograms

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Area of a ParallelogramLet's use the same process as we did for the rectangle. How many 1 ft 2 tiles fit across the bottom of the parallelogram?

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Area of a ParallelogramLet's use the same process as we did for the rectangle. If we build the parallelogram with rows of 14 ft 2, what happens?

How tall is the parallelogram?How can you tell?

14 ft

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How does this help us find the area of the parallelogram?

14 ft

How do you find the area of a parallelogram?

4 ft

Area of a Parallelogram

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A = base(height)A = bh

The Area (A) of a parallelogram is found by using the formula:

Note: The base & height always form a right angle !

Area of a Parallelogram

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Example.

Find the area of the figure.

4 cm

4 cm

2.2 cm 2.2 cm1.9 cm

click

Area of a Parallelogram

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4

Try These.

Find the area of the figures.

8

75

11 m

14 m

11 m

20 m

click click

Area of a Parallelogram

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59 Find the area.

11 ft 10 ft

12 ft

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60 Find the area.

17 in

17 in

10 in 12 in12 in

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61 Find the area.

7 m

13 m 13 m

7 m

11 m

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62 Find the area.

12 cm

11 cm

9 cm

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Area of Triangles

Return to Table of Contents

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Area of a TriangleLet's use the same process as we did for the rectangle & parallelogram. How many 1 ft 2 tiles fit across the bottom of the triangle?

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Area of a TriangleIf we continue to build the triangle with rows of 10 ft 2, what happens?

How tall is the triangle? How can you tell?

10 ft

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How does this help us find the area of the triangle?

Find the area of the rectangle, then divide by 220 ft2

See that the rectangle we built is twice as large as the triangle. How do you find the area of a triangle?

10 ft

4 ft

Area of a Triangle

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Is this true for all triangles?Let's see!

Calculating base(height) results in 2 triangles!

Area of a Triangle

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The Area (A) of a triangle is found by using the formula:

Note: The base & height always form a right angle!

Area of a Triangle

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Example.

Find the area of the figure.

4 cm

5 cm 5 cm

6 cm

4

24

12

click

Area of a Triangle

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Try These.

Find the area of the figures.

13 ft

11 ft

9 ft 12 ft

1420

16

15

click

click

Area of a Triangle

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63 Find the area.

8 in

5 in

11 in 10 in

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64 Find the area.

15 m

8 m9 m 12 m

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Area of Trapezoids

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Area of a Trapezoid· Cut the trapezoid in half horizontally· Rotate the top half so it lies next to the bottom half· A parallelogram is created

See the diagrams below

Base1

Base2

Height

Base1Base2

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The Area (A) of a trapezoid is found by using the formula:

Note: The bases & height always form a right angle!

Area of a Trapezoid

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Example.

Find the area of the figure.

12 cm

10 cm 11 cm

9 cm

click

Area of a Trapezoid

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Try These.

Find the area of the figures.

13 ft

11 ft

9 ft 11 ft

20

15

11 ft 9 117

click click

Area of a Trapezoid

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65 Find the area of the trapezoid.

4 m

10 m

6.5 m

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66 Find the area of the trapezoid.

22 cm

14 cm

8 cm

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Area of Circles

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Area of a Circle

The Area (A) of a Circle is found by solving the following formula:

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7 cm

Area of a Circle

Find the area of the circle.A = # r2

1. Substitute the radius into formula.A = # (7)2

2. Use 3.14 as an approximation for # .A = 3.14(49)A = 153.86 cm2

3. Don't forget to label the units as square units.

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67 What is the Area (A) of a Circle with a radius (r) of 8 m?Use 3.14 as your value of # .

8 m

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68 What is the Area (A) of the circle? Use 3.14 as your value of # .

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69 What is the Area (A) of the circle? Use 3.14 as your value of # .

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70 A circular sprinkler sprays water with a radius of 11 ft. How much area can the sprinkler cover? Use 3.14 as your value of # .

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71 What is the area of a circle with a diameter of 24 yds? Use 3.14 as your value of # .

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72 What is the radius of a circle whose area is 254.34 mm2? Use 3.14 as your value of # .

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73 A circular pool has an area of 153.86 ft2.What is its diameter? Use 3.14 as your value of # .

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Similar to when we found the circumference of a circle, with the area, you could be asked to "Leave your answer in terms of π".

Click here if you need to review that property.

Answer in Terms of π

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Find the area of the circle.A = # r2

1. Substitute the radius into formula.A = # (7)2

2. Evaluate the arithmetic operations excluding # .

A = # (49)A = 49# cm2

3. Don't forget to label the units as square units.

7 cm

Answer in Terms of π

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74 What is the Area (A) of a Circle with a radius (r) of 8 m?Leave your answer in terms of π.

8 m

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75 What is the Area (A) of the circle? Leave your answer in terms of π.

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76 What is the Area (A) of the circle? Leave your answer in terms of π.

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77 A circular sprinkler sprays water with a radius of 13 ft. How much area can the sprinkler cover? Leave your answer in terms of π.

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78 What is the area of a circle with a diameter of 24 yds? Leave your answer in terms of π.

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79 What is the radius of a circle whose area is 225π mm2?

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80 A circular pool has an area of 81π ft2.What is its diameter?

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81 A circular mirror has a diameter of 12 inches.

Part AWhat is the area, in square inches, of the mirror?

A 6π

B 12π

C 36π

D 72π

From EOY PARCC sample test calculator #5

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82 A circular mirror has a diameter of 12 inches.

Part BA circular frame that is 3 inches wide surrounds the mirror. What is the combined area, in square inches, of the circular mirror and the frame?

A 9π

B 18π

C 54π

D 81π

From EOY PARCC sample test calculator #5

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Mixed Review:Perimeter,

Circumference & Area

Return to Table of Contents

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83 Dr. Dan wants to keep his kitten from running through his flower bed by putting up some fencing. The flower bed is 10 ft. by 6 ft. Will Dr. Dan need to know the area or the perimeter of his flower bed to keep his kitty from trampling the flowers?

A Area

B Perimeter

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84 Now solve the problem....

Dr. Dan wants to keep his kitten from running through his flower bed by putting up some fencing. The flower bed is 10 ft. by 6 ft. How much fencing will he need?

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85 Find the perimeter of the figure.

5 cm

4 cm 3 cm 4 cm

11 cm

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86 Find the area of the figure.

4 yd

8 yd

9 yd

8 yd

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87 Find the perimeter of the figure.

4 m

7 m

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88 Find the circumference of the figure. Use 3.14 as your value of # .

12 in

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89 Find the area of the figure.

9 in 5 in

12 in

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90 Find the area of the figure.

5 cm

4 cm 3 cm 4 cm

11 cm

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91 Find the perimeter of the figure.

9 in 5 in

12 in

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92 Find the perimeter of the figure.

4 yd

8 yd

9 yd

8 yd

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93 Find the area of the figure. Use 3.14 as your value of # .

12 in

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94 Find the area of the figure.

4 m

7 m

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95 If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, how far from the edge of the door should you put the edge of the bar?

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96 A wall is 48" wide. You want to center a picture frame that is 20" wide on the wall. How much space will there be between the edge of the wall and the frame?

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Area ofIrregular Figures

Return to Table of Contents

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Area of Irregular FiguresMethod #1

1. Divide the figure into smaller figures (that you know how to find the area of)

2. Label each small figure and find the area of each

3. Add the areas

4. Label your answer

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Example:Find the area of the figure.

10 m

6 m

3 m2 m

10 m

6 m

3 m2 m #1

#2

Area of Irregular Figures

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Area of Irregular FiguresMethod #2

1. Create one large, closed figure.

2. Label the small added figure and find the area.

3. Find the area of the new, large figure

4. Subtract the areas

5. Label your answer

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Example:Find the area of the figure.

10 m

6 m

3 m2 m

10 m

6 m

3 m2 m Whole

RectangleExtra

Rectangle

Area of Irregular Figures

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Try This:Find the area of the figure.

2m

4m

2m5m

Area of Irregular Figures

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Try This:Find the area of the figure.

20 ft

16 ft

8 ft

10 ft

Area of Irregular Figures

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97 Find the area.

4'

2.5'

1.5'

2.5'

8.75'

7.75'

5.25'

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98 Find the area.

16

121925

35

13

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99 Find the area.

8 cm 58 cm

15 cm

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100 Find the area. Use 3.14 as your value of # .4 ft.

9 ft.

5 ft.

6 ft.

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Area of Shaded Regions

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Area of a Shaded Region

1. Find area of whole figure.

2. Find area of unshaded figure(s).

3. Subtract unshaded area from whole figure.

4. Label answer with units 2

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Example

Find the area of the shaded region.

15 ft

20 ft

7 ft7 ft

Area Whole Rectangle

Area Unshaded Square

Area Shaded Region

Area of Shaded Region

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Try This

Find the area of the shaded region.Use 3.14 as your value of # . Area Whole Square

Area Circle

Area Shaded Region14 cm

Area of Shaded Region

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Try This

Find the area of the shaded region. Area Trapezoid

Area Rectangle

Area Shaded Region

20 m

12 m3 m

8 m2 m

Area of Shaded Region

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101 Find the area of the shaded region.

6'

8'

2'4'

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102 Find the area of the shaded region.

11"

12"

8"7"

6"

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12"

14"

8"

6"

8"

4"

103 Find the area of the shaded region.

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104 Find the area of the shaded region. Use 3.14 as your value of # .

4 yd

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105 A cement path 3 feet wide is poured around a rectangular pool. If the pool is 15 feet by 7 feet, how much cement was needed to create the path?

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106 This figure shows two shaded regions and a non-shaded region. Angles in the figure that appear to be right angles are right angles.

Part AWhat is the area, in square inches, of the triangular-shaped region that is shaded in this figure? Type in your number answer.

From PARCC EOY sample test calculator #16

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107 This figure shows two shaded regions and a non-shaded region. Angles in the figure that appear to be right angles are right angles.

Part BWhat is the area, in square inches, of the non-shaded region in this figure? Type in your number answer.

From PARCC EOY sample test calculator #16

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Glossary

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Instruction

Adjacent Angles

a

ba b a

b

Two angles that are next to each other and have a common ray between them.

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Alternate Exterior AnglesWhen two lines are crossed by a transversal the pairs of angles on opposite sides of the

transversal but outside the two lines.

a

b c

d

a b c d

a b

c d

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Alternate Interior Angles When two lines are crossed by a transversal, the pairs of angles on opposite sides of the

transversal but inside the two lines.

a b c

d a b c d a b

c d

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Angle

The intersection of 2 rays with a common endpoint.

A

∠A

B

DC

∠BCD, ∠DCB or ∠C

E

GF

2

∠EFG, ∠GFE, ∠F, or ∠2

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The number of square units (units2) it takes to cover the surface of a figure

Area

Area = 6 units2

Area = 8 units2 Area = 16 units2

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Area of a Circle

Radius

4

A = (4)2A = 16 u2

A ≈ 50.24 u2

12 d = 12r = 6

A = (6)2A = 36 u2

A ≈ 113.04 u2

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Area of a Parallelogram

A = base(height)A = bh

b

h6

8

8

10

A = 6(8)A = 48 units2 A = 8(10)

A = 80 units2

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Area of a Rectangle

A = length(width)A = lw

l

w

8

3

A = 8(3)A = 24 units2

10

4

A = 10(4)A = 40 units2

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Area of a Square

A = side(side)A = s2

s

s

s

s

2

5

A = 22

A = 4 units2 A = 52

A = 25 units2

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Area of a Trapezoid

A = 1 2

(b1 + b2)(h)

b1

b2

hb1b2

hb1

b2

h

A = 1 2

h(b1 + b2)or

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Area of a Triangle

A = bh 1 2 A = bh

2or

h

b

h

b bh

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The outer boundary of a circle. The "perimeter" of the circle.

Circumference

C = 2 r C = d

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Way to Remember:

By drawing the extraline w/ the "C", you

form a 9, for 90°

Complimentary Angles

Two angles with a sum of 90 degrees.

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38°

38°

A

B∠A ≅ ∠B

C

D

∠C ≅ ∠D

E

F∠E ≅ ∠F

Angles that have the same measurement.The symbol for congruent is "≅".

Congruent angles can be shown with the same degree measurement, or marked

with the same number of arcs.

Congruent Angles

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Corresponding Angles

Angles that are on the same side of the transversal and in the same location at

each intersection.

a

a

b

b c

c d

d

a a b b c c d d a

a b

b c

c d

d

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Any straight line segment that passes through the center of the circle, whose endpoints are on

the circle.

Diameter

d = 14 units d = 11 units

14 11Diameter

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Perimeter

The distance around a two-dimensional figure.Found by adding up all of the sides.

ab

c

P = a + b + c

a

b

P = a + b + a + bP = 2a + 2b

a

b

a

aa

a

aa

P = a + a + a + a + a + aP = 6a

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Pi ( )

A mathematical constant; the ratio of a circle's circumference to its diameter.

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Any line segment from the center of the circle, to any point on the circle.

The radius is 1/2 of the diameter.

Radius

Radius

r = 7 units r = 5.5 units

7 11

d = 11r = 1/2(11)

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Same Side Interior Angles When two lines are crossed by a transversal, the pairs of angles on the same side of the

transversal but inside the two lines.

a b

c d a b

c d

a b c

d

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+

180o

=

90o 90o+

180o

=

80o100o SWay to

Remember:

By drawing the extraline w/ the "S", you

form an 8, for 180°

Supplementary Angles

Two angles with a sum of 180 degrees.

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Transversal

A line that cuts across two or more (usually parallel) lines.

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Vertical AnglesTwo angles that are opposite

each other when two lines intersect.

Way to Remember:

Vertical angles form 2 "V's" going in

opposite directions

120o

120o

60oX

x = 60o

70o

70o

110o110o

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