Section 1-4 Pairs of Angles

Adjacent Angles Definition: A pair of angles with a shared vertex and common side but do not have overlapping interiors. Example 1: 1 and 2 are adjacent. 3 and 4 are not. 1 and ADC are not adjacent. 4 3 Adjacent Angles( a common side ) Non-Adjacent Angles

Linear Pair A Linear Pair is a pair of adjacent angles whose non common sides are opposite rays, which form a 180 degree angle.

Example 1 Tell whether the pair of angles are adjacent, adjacent and form a linear pair, not adjacent, or form a linear pair and Adjacent AND Linear Pair and Not Adjacent and Adjacent

Complementary Angles Definition: Examples: Adjacent Angles A pair of angles whose sum is 90˚. **The angles DO NOT have to be adjacent!!** Examples: Adjacent Angles ( a common side ) Non-Adjacent Angles

Complementary Angles Some examples of complementary angles are shown below. 75° I mH + mI = 90 15° H 50° H 40° Q P S mPHQ + mQHS = 90 30° 60° T U V W Z mTZU + mVZW = 90

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

Supplementary Angles Some examples of supplementary angles are shown below. 105° H 75° I mH + mI = 180 50° H 130° Q P S mPHQ + mQHS = 180 60° 120° T U V W Z mTZU + mUZV = 180 and mTZU + mVZW = 180

Vertical Angles Definition of Two angles are vertical iff they are two nonadjacent angles formed by a pair of intersecting lines. Vertical angles are ALWAYS CONGRUENT!! Vertical angles: 1 and 3 1 4 2 2 and 4 3

“Think and Discuss” (Grey Box) Assignment #8 Pg. 31 “Think and Discuss” (Grey Box) #1-3

Example 1 Name each pair of vertical angles.

Example 2 Find the measure of the following: A complement of this angle: A supplement of this angle:

Example 3 Find the measure of the following: A complement of this angle: A supplement of this angle:

Example 4 An angle measures three degrees less than twice the measure of its complement. Find the measure of it’s complement.

Example 5 An angle measures 12 degrees more than ½ the measure of it’s supplement. Find the measure of the angle.