1 5 Exploring Angle Pairs Adjacent Angles Definition

1. 5 Exploring Angle Pairs

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

Examples < C and < D are supplementary angles. Find m < C & m < D.

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