1.4 – Measure and Classify Angles &Angle Constructions

1.5 –Describe Angle Pair Relationships

Angle: Two different rays with the same initial point. Measured in degrees.

A, BAC, CAB, 1

B

A1

C

Vertex

Sides

Common initial point, where rays meet

The rays of the angle

vertex

pt. A

side

side

AB

AC

AC

B

AC

B

Acute

Right

Obtuse

Straight

Angle more than 0°, but less than 90°

Angle more than 90°, but less than 180°

Angle that measures 90°

Angle that measures 180°

AmA = 50°

RmR = 90°

OmO = 110°

SmS = 180°

Angle Bisector

Ray that cuts an angle in half to make 2 congruent angles

P

Q R

S

QS bisects PQR

PQS SQR

Adjacent angles

Two angles that share a common side and vertex

12

1 is adjacent to

2

Complementary Angles: Two angles that add to 90°

m1 + m2 = 90°

12

1

2

Supplementary Angles: Two angles that add to 180°

m1 + m2 = 180°

1 21

2

Linear Pair: Supplementary angles that are adjacent

1 2

m1 + m2 = 180°

Vertical Angles: Two angles whose sides form two pairs of opposite rays

12

They will always be congruent!

21

Angle Addition Postulate:

If you add two adjacent angles, it totals to get their sum.

A

B

C

D

mABC + mCBD = mABD

1. Give three names for the angle shown, then name the vertex and sides.

DEF

FED

E

Pt. E ED

EF

Names Vertex Sides

1. Give three names for the angle shown, then name the vertex and sides.

QVS

SVQ

V

Pt. V VQ

VS

Names Vertex Sides

2. Classify the angle as acute, right, obtuse or straight.

mA = 115°

obtuse

2. Classify the angle as acute, right, obtuse or straight.

mA = 90°

right

2. Classify the angle as acute, right, obtuse or straight.

mA = 85°

acute

2. Classify the angle as acute, right, obtuse or straight.

mA = 180°

straight

3. Use a protractor to find the measure of the angle to the nearest degree. Then classify the angle as acute, obtuse, straight, or right.

91° obtuse

3. Use a protractor to find the measure of the angle to the nearest degree. Then classify the angle as acute, obtuse, straight, or right.

32° acute

3. Use a protractor to find the measure of the angle to the nearest degree. Then classify the angle as acute, obtuse, straight, or right.

180° straight

4. Find the indicated measure.

mPRS = 81+42

mPRS = 123°

4. Find the indicated measure.

mWXZ = 90 – 26 =

mWXZ = 64°

5. Find each indicated angle.

15°

15°

75° 90°

90°

5. Find each indicated angle.

a = 180-160 = 20°

20°

b = 180-20 = 160°

160°

c = 180-90-75 = 15°

d = 180-90-15 = 75°

15°

mNRP + mPRQ = mNRQ 8x + 7 + 4x – 1 = 78

12x + 6 = 7812x = 72

x = 6

mPRQ = 4(6) – 1

mPRQ = 24 – 1mPRQ = 23°

mADB + mBDC = mADC 11x – 7 + 5x – 3 = 118

16x – 10 = 11816x = 128

x = 8

mADB = 11(8) – 7

mADB = 88 – 7mADB = 81°

mABC =

5x + 2 = 7x – 6

2 = 2x – 6

8 = 2x4 = x

44°5(4)+2 + 7(4)-6 = 20+2 +28-6 =

5x + 13 = 9x – 23

13 = 4x – 23

36 = 4x9 = x

mABC = 116°5(9)+13 + 9(9)-23 = 45+13+81-23 =

8. Tell whether the indicated angles are adjacent.

EFG and HGF

no

8. Tell whether the indicated angles are adjacent.

JNM and MNK

yes

9. Name a pair of complementary angles, supplementary angles, and vertical angles .

Complementary:QOR and ROL

Supplementary:ROL and LON

ROM and MON

Vertical:

L

M

N

PQ

R OMON and NOP

QOL and LOM

ROL and NOP

LOM and QOP

9. Name a pair of complementary angles, supplementary angles, and vertical angles .

Complementary:DGE and EGA

Supplementary:DGE and EGB

DGA and AGB

Vertical:

EGA and AGC

DGE and BGC

EGB and DGCA

B

C

D

E

G

10. 1 and 2 are complementary angles. Given the measure of 1, find m2.

m1 = 82°

m2 = 8°90 – 82 =

10. 1 and 2 are complementary angles. Given the measure of 1, find m2.

m2 = 67°90 – 23 =

m1 = 23°

11. 1 and 2 are supplementary angles. Given the measure of 1, find m2.

m2 = 98°180 – 82 =

m1 = 82°

m2 = 75°180 – 105 =

m1 = 105°

11. 1 and 2 are supplementary angles. Given the measure of 1, find m2.

12. Find the measure of ABD and DBC.

4x + 6 + 11x – 6 = 180

15x = 180x = 12

mABD = 4(12)+6= 48+6= 54°

mDBC = 11(12)-6= 132-6= 126°

12. Find the measure of ABD and DBC.

2x + 3x = 90

5x = 90x = 18

mABD = 2(18)= 36°

mDBC = 3(18)= 54°

13. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither.

1 and 2

Linear pair

13. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither.

2 and 4

Vertical angles

6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither.

5 and 8

neither

7. Find the values of x and y.

6x – 11 + 2x – 9 = 180

8x – 20 = 180 8x = 200

x = 25°

20y + 19 + 2x – 9 = 18020y + 19 + 2(25) – 9 = 180

20y + 60 = 180

20y = 120y = 6°

7. Find the values of x and y.

9x + 2 + 10x + 7 = 180

19x + 9 = 18019x = 171

x = 9°

18y + 25 + 9x + 2 = 180

18y + 25 + 9(9) + 2 = 180

18y + 108 = 180

18y = 72y = 4°

HW Problem

1.4 # 38

1.41.5

28-3238-41

4-18 even, 21, 22, 24-27, 33-38 (draw pic), 40, 414, 5, 7-33 odd, 49-52, 61, 62

**Bring compass and ruler tomorrow! Books will not be needed

53°

37°