Chapter 1 Section 1.5 Angle Pair Relationships
Jan 13, 2016
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