1. 1.5 Exploring Angle Pairs

2. Adjacent Angles Two angles that share a common vertex and Definition:
side but no common interior points.
Definition:
Examples: 4 3
Adjacent Angles( a common side )
1 and 2 are adjacent.
Non-Adjacent Angles
1 and ADC are not adjacent.
3 and 4 are not adjacent.

3. Complementary Angles Definition: A pair of angles whose sum is 90˚
Examples:
Adjacent Angles
( a common side )
Non-Adjacent Angles

4. Supplementary Angles Definition: A pair of angles whose sum is 180˚
Examples:
Adjacent supplementary angles are also called “Linear Pair.”
Non-Adjacent Angles

5. Examples
< 1 and < 2 are complementary angles. Given m < 1, find m < 2. a. b.
< 3 and < 4 are supplementary angles. Given m < 3, find m < 4. a. b.

6. Examples
< A and < B are complementary angles. Find m < A & m < B.
5𝑥+4+7𝑥−10=90
12𝑥−6=90
12𝑥=96
𝑥=8
𝑚<𝐴=5 8 +4
𝑚<𝐵=7 8 −10
𝑚<𝐴=40+4
𝑚<𝐵=56−10
𝑚<𝐴=44
𝑚<𝐵=46

7. Examples < C and < D are supplementary angles.
Find m < C & m < D.
7𝑥−3+𝑥−1=180
8𝑥−4=180
8𝑥=184
𝑥=23
𝑚<𝐶=7 23 −3
𝑚<𝐵= 23 −1
𝑚<𝐴=161−3
𝑚<𝐵=23−1
𝑚<𝐴=158
𝑚<𝐵=22

8. Linear Pair Definition: Two adjacent angles are a linear pair if their
non-common sides are opposite rays.
The angles in a linear pair are supplementary.

9. Vertical Angles Definition: A pair of angles whose sides
form opposite rays.
Vertical angles are congruent.
Vertical angles are non-adjacent angles formed by intersecting lines.

10. Examples What are the linear pairs? <4 and <5
What are the vertical angles?
<1 and <5

11. Examples < 1 & < 3 < 2 & < 3 < 4 & < 5
< 8 & < 5
< 6 & < 7
< 4 & < 9
< 1 & < 2 & < 3
neither
neither
Linear pair
Vertical angles
Linear pair
Vertical angles
neither

12. Example: If m4 = 67º, find the measures of all other angles.
Step 1: Mark the figure with given info.
Step 2: Write an equation.
67º

13. Example: If m1 = 23 º and m2 = 32 º, find the measures of all other angles.
Answers:

14. Example: If m  1 = 44º, m  7 = 77º find the measures of all other angles.
Answers: