Geometry 1 6 Angle Pair Relationships VERTICAL ANGLES

Geometry 1. 6 Angle Pair Relationships

VERTICAL ANGLES Vertical angles are two angles whose sides form two pairs of opposite rays. 1 2 4 3

LINEAR PAIR Linear pair are two adjacent angles whose noncommon sides are opposite rays.

Example a) b) c) d) Are angle EOD and angle COD a linear pair? Are angle AOB and angle BOC a linear pair? Are angle EOD and angle AOB vertical angles? Are angle AOE and angle COD vertical angles?

Example The measure of angle 1 is 36 degrees. Find the measures of the other three angles.

Example Solve for x and y. Then find the angle measures. (4 x + 15) (5 x + 30) (3 y + 15) (3 y - 15)

COMPLEMENTARY ANGLES Two angles are complementary angles if the sum of their measures is 90 degrees. Each angle is the complement of the other. Complementary angles can be adjacent or nonadjacent.

SUPPLEMENTARY ANGLES Two angles are supplementary angles if the sum of their measures is 180 degrees. Each angle is the supplement of the other. Supplementary angles can be adjacent or nonadjacent.

Example a) Given that angle G is a supplement of angle H and measure of angle G is 82 degrees, find the measure of angle H. b) Given that angle U is a complement of angle V and measure of angle U is 73 degrees, find the measure of angle V.

Example Angle W and angle Z are complementary. The measure of angle Z is five times the measure of angle W. Find the measure of angle W.

Example Angle T and angle S are supplementary. The measure of angle T is half the measure of angle S. Find the measure of angle S.