1. Angle Pair Relationships
Chapter 1 Section 1.6
Angle Pair Relationships

2. Warm-Up

3. 1 and 2 form a linear pair
m1 + m2 =180°
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°.

4. Vertical Angles 1 2 3 4
1 and 3 are vertical angles
4 and 2 are vertical angles
Two angles are vertical if their sides form two pairs of opposite rays.
Vertical Angles are congruent

5. Use the figure to answer the questions
Are 1 and 2 a linear pair?
Yes
Are 4 and 5 a linear pair? No
Are 3 and 1 vertical angles?
Are 2 and 5 vertical angles?

6. Use the figure to answer the questions
If m6 = 51°, then m7 = _____
129° -- Linear Pair
If m8 = 103°, then m6 =_____
103° -- Vertical Angles
If m9 = 136°, then m8 =_____
44° -- Linear Pair
If m7 = 53°, then m9 =_____
53° -- Vertical Angles

7. A and B are complementary
Complementary Angles A
30°
60° B
mA + mB = 90 °
A and B are complementary
Two angles are complementary if their sum is 90°.
Each Angle is the complement of the other

8. A and B are complementary
Supplementary Angles A
120°
60° B
mA + mB = 180 °
A and B are complementary
Two angles are supplementary if their sum is 180°.
Each angle is the supplement of the other

9. A and B are complementary and B and C are supplementary
If mA = 48° then mB = _____ and mC = _____
mA + mB = 90°
48° + mB = 90°
mB = 42°
mB + mC = 180°
42° + mC = 180°
mC = 138°

10. A and B are complementary and B and C are supplementary
If mB = 83° then mA = _____ and mC = _____
mA + mB = 90°
mA + 83° = 90°
mA = 7°
mB + mC = 180°
83° + mC = 180°
mC = 97°

11. A and B are complementary and B and C are supplementary
If mC = 127° then mB = _____ and mA = _____
mC + mB = 180°
127° + mB = 180°
mB = 53°
mA + mB = 90°
mA + 53° = 90°
mA = 37°

12. A and B are complementary and B and C are supplementary
If mA = 25° then mB = _____ and mC = _____
mA + mB = 90°
25° + mB = 90°
mB = 65°
mB + mC = 180°
65° + mC = 180°
mC = 115°

13. Find the value of the variable
Vertical Angles are congruent
Solve for x
2x + 40 = 110
2x = 70
x = 35°
Solve for y
y + 20° = 70°
y = 50°

14. Find the value of the variable
Linear Pairs are add up to 180°
Vertical Angles are congruent
x + 168° = 180°
x = 12°
y = 168°

15. Find the value of the variable
Vertical Angles are congruent
Solve for x
48 + x = 64
x = 16
Solve for y
8y + 36 = 14y – 24
36 = 6y – 24
60 = 6y
10 = y