Simplify each expression. 1. 90 – ( x + 20) 2. 180 – (3 x – 10)

Holt McDougal Geometry

1-4 Pairs of Angles

Simplify each expression.

1. 90 – (x + 20)

2. 180 – (3x – 10)

Write an algebraic expression for each of the following.

3. 4 more than twice a number

4. 6 less than half a number

70 – x

190 – 3x

2n + 4

Flashback

Holt McDougal Geometry

1-4 Pairs of Angles

Identify adjacent, vertical, complementary, and supplementary angles.

Find measures of pairs of angles.

GOALS!

Holt McDougal Geometry

1-4 Pairs of Angles

Draw an example of adjacent angles.

Draw an example of a linear pair.

Holt McDougal Geometry

1-4 Pairs of Angles

Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.

Example 1: Identifying Angle Pairs

AEB and BED

Adjacent and form a linear pair

Holt McDougal Geometry

1-4 Pairs of Angles

Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.

Example 2: Identifying Angle Pairs

AEB and BEC

Only adjacent

Holt McDougal Geometry

1-4 Pairs of Angles

DEC and AEB

Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.

Example 3: Identifying Angle Pairs

Not Adjacent

Holt McDougal Geometry

1-4 Pairs of Angles

5 and 6

Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.

Adjacent and form a linear pair

Check Up

Holt McDougal Geometry

1-4 Pairs of Angles

7 and SPU

Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.

Not adjacent

Check Up

Holt McDougal Geometry

1-4 Pairs of Angles

7 and 8

Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.

Not adjacent

Check Up

Holt McDougal Geometry

1-4 Pairs of Angles

Complementary angles-

What is the complement of 30⁰?

What is the complement of 44.2⁰?

Holt McDougal Geometry

1-4 Pairs of Angles

Complementary angles-

What is the complement of 30⁰?

What is the complement of 44.2⁰?

What is the complement of

Holt McDougal Geometry

1-4 Pairs of Angles

Supplementary angles-

What is the supplement of 30⁰?

What is the supplement of 44.2⁰?

What is the supplement of

Holt McDougal Geometry

1-4 Pairs of Angles

Warm Up

1.) Find the complement of an angle that measures 30°.

2.) Find the supplement of an angle that measures 100°.

Holt McDougal Geometry

1-4 Pairs of Angles

Find the measure of each of the following.

Example 4: Finding the Measures of Complements and Supplements

A. complement of F

B. supplement of G

90 – 59 = 31

(180 – x)

180 – (7x+10) = 180 – 7x – 10

= (170 – 7x)

(90 – x)

Holt McDougal Geometry

1-4 Pairs of Angles

a. complement of E

Find the measure of each of the following.

b. supplement of F

= (102 – 7x)°

180 – 116.5° =

90° – (7x – 12)° = 90° – 7x° + 12°

(90 – x)°

(180 – x)

Check Up

Holt McDougal Geometry

1-4 Pairs of Angles

Find the measure of each of the following.

Example 3: Using complements and supplements

A. Find the value of b.

B. Find the value of x

b = 27

93 + 3x + 18 = 180

X = 23

63 + b = 90

Holt McDougal Geometry

1-4 Pairs of Angles

Example 6 ∠R and ∠S are complementary. If m∠R = 7 + 3x and m∠S = 2x + 13. What is the value of x. Find the measure of both angles.

7 + 3x + 2x + 13 = 90

x = 14

Set up the equation!

Solve for x!

R = 49 and 41

Holt McDougal Geometry

1-4 Pairs of AnglesCheck Up

∠DEF and ∠FEG are supplementary. m∠DEF = 9x + 1 and m∠FEG = 8x + 9. Find the measure of both angles.

x = 10 ∠DEF = 91 and ∠FEG =89

Holt McDougal Geometry

1-4 Pairs of Angles

Light passing through a fiber optic cable reflects off the walls of the cable in such a way that 1 ≅ 2, 1 and 3 are complementary, and 2 and 4 are complementary.

If m1 = 47°, find m2, m3, and m4.

Example 7: Problem-Solving Application

m2 = 47°, m3 = 43°, and m4 =43°.

Holt McDougal Geometry

1-4 Pairs of Angles

What if...? Suppose m3 = 27.6°. Find m1, m2, and m4.

Check Up

Thus m1 = m2 = 62.4°; m4 = 27.6°.

Holt McDougal Geometry

1-4 Pairs of Angles

Assignment: Page 32 14-21,26-31

Holt McDougal Geometry

1-4 Pairs of Angles

Warm up

The measurement of angle A is 64.1° and the measurement of angle B is (4x – 30)°.

1.) Find the supplement of angle A.

2.) Find the complement of angle B.

Holt McDougal Geometry

1-4 Pairs of Angles

Day 2 Vertical Angles

Holt McDougal Geometry

1-4 Pairs of Angles

Need: straightedge and protractor

Draw large X.

Number the angles 1, 2,3,4

Measure all four angles

What is the result?

Look through the basic terms, what type of angles are these?

Holt McDougal Geometry

1-4 Pairs of Angles

Vertical angles

A and C are vertical angles, as are B and D.

Name two sets of vertical angles

What do you know about ∠A and ∠C?

What do you know about ∠B and ∠D?

Holt McDougal Geometry

1-4 Pairs of Angles

Lesson Quiz: Part I

mA = 64.1°, and mB =(4x – 30)°. Find the measure of each of the following.

1. supplement of A

2. complement of B

3. Determine whether this statement is true or false. If

false, explain why. If two angles are

complementary and congruent, then the measure

of each is 90°.

(120 – 4x) °

115.9°

False; each is 45°.

Holt McDougal Geometry

1-4 Pairs of Angles

Lesson Quiz: Part II

mXYZ = 2x° and mPQR = (8x - 20)°.

4. If XYZ and PQR are supplementary, find the measure of each angle.

5. If XYZ and PQR are complementary, find the measure of each angle.

22°; 68°

40°; 140°

Holt McDougal Geometry

1-4 Pairs of Angles

Warm Up

The measurement of angle XYZ = 2x° and the measurement of angle PQR = (8x – 20)°.

1.)If XYZ and PQR are supplementary find the measure of each angle.

2.) If XYZ and PQR are complementary, find the measure of each angle.