1.5 –Describe Angle Pair Relationships

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 2

1

2

Linear Pair: Two adjacent angles whose noncommon sides are opposite rays

1 2

They will always add to 180°

m1 + m2 = 180°

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

12

They will always be congruent!

21

1. Tell whether the indicated angles are adjacent.

EFG and HGF

no

1. Tell whether the indicated angles are adjacent.

JNM and MNK

yes

2. 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 O

MON and NOP

QOL and LOM

ROL and NOP

LOM and QOP

2. 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 DGC

A

B

C

D

E

G

3. 1 and 2 are complementary angles. Given the measure of 1, find m2.

m1 = 82°

m2 = 8°90 – 82 =

3. 1 and 2 are complementary angles. Given the measure of 1, find m2.

m2 = 67°90 – 23 =

m1 = 23°

4. 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°

4. 1 and 2 are supplementary angles. Given the measure of 1, find m2.

5. 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°

5. Find the measure of ABD and DBC.

2x + 3x = 90

5x = 90x = 18

mABD = 2(18)= 36°

mDBC = 3(18)= 54°

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

1 and 2

Linear pair

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

1 and 3

Vertical angles

6. 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 7

neither

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.

16x + 9x + 5 = 180

25x + 5 = 18025x = 175

x = 7°

16x + 4y = 180

16(7) + 4y = 180

112 + 4y = 180

4y = 68y = 17°

7. Find the values of x and y.

6x – 11 + 2x – 9 = 180

8x – 20 = 180 8x = 200

x = 25°

20y + 19 + 2x – 9 = 180

20y + 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

# 49

1.5 38-41 1-5, 7-33 odd, 39-43 odd, 49-53, 61, 62

Ans:

ex: FGA & AGC

supplementary**Bring calculator tomorrow