Chapter 1Section 1.5

Angle Pair Relationships

Linear Pair

• Two adjacent angles form a linear pair if their noncommon sides are opposite rays.– Form a straight angle.

• Any two angles that form a linear pair have a sum of 180°.

1 and 2 form a linear pair

m1 + m2 =180°

1 2

Vertical Angles

• Two angles are vertical if their sides form two pairs of opposite rays.

• Vertical Angles are congruent

12

34

1 and 3 are vertical angles

4 and 2 are vertical angles

Use the figure to answer the questions

1. Are 1 and 2 a linear pair?

• Yes

2. Are 4 and 5 a linear pair?

• No

3. Are 3 and 1 vertical angles?

• No

4. Are 2 and 5 vertical angles?

• Yes

Use the figure to answer the questions

5. If m6 = 51°, then m7 = _____

• 129° -- Linear Pair

6. If m8 = 103°, then m6 =_____

• 103° -- Vertical Angels

7. If m9 = 136°, then m8 =_____

5. 44° -- Linear Pair

• If m7 = 53°, then m9 =_____

5. 53° -- Vertical Angles

Complementary Angles

• Two angles are complementary if their sum is 90°.

• Each Angle is the complement of the other

mA + mB = 90 °

A and B are complementary

30°

60°

A

B

Supplementary Angles

• Two angles are supplementary if their sum is 180°.

• Each angle is the supplement of the other

mA + mB = 180 °

A and B are complementary

120°60°

A

B

A and B are complementary and B and C are supplementary

9. If mA = 48° then mB = _____ and mC = _____

• mA + mB = 90°

• 48° + mB = 90°

• mB = 42°

• mB + mC = 180°

• 42° + mC = 180°

• mC = 138°

A and B are complementary and B and C are supplementary

10. If mB = 83° then mA = _____ and mC = _____

• mA + mB = 90°

• mA + 83° = 90°

• mA = 7°

• mB + mC = 180°

• 83° + mC = 180°

• mC = 97°

A and B are complementary and B and C are supplementary

11. If mC = 127° then mB = _____ and mA = _____

• mC + mB = 180°

• 127° + mB = 180°

• mB = 53°

• mA + mB = 90°

• mA + 53° = 90°

• mA = 37°

A and B are complementary and B and C are supplementary

12. If mA = 25° then mB = _____ and mC = _____

• mA + mB = 90°

• 25° + mB = 90°

• mB = 65°

• mB + mC = 180°

•65° + mC = 180°

• mC = 115°

Find the value of the variable

Vertical Angles are congruent

Solve for y

y + 20° = 70°

y = 50°

Solve for x

2x + 40 = 110

2x = 70

x = 35°

Find the value of the variable

Linear Pairs are add up to 180°

x + 168° = 180°

x = 12°

Vertical Angles are congruent

y = 168°

Find the value of the variable

Solve for x

48 + x = 64

x = 16

Vertical Angles are congruent

Solve for y

8y + 36 = 14y – 24

36 = 6y – 24

60 = 6y

10 = y

Homework #6 Pg 38: 1-7, 9-15

odd, 16, 17-27 odd, 28-35, 46-54, 57,61