1.5 Exploring Angle Pairs

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.

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

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

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.

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

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

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.

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.

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

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

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

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

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