1 6 Describing Pairs of Angles Vocabulary Adjacent

1. 6 Describing Pairs of Angles

Vocabulary • Adjacent Angles—Two angles that share a common vertex and side, but have no common interior points Adjacent Angle vs. Nonadjacent Angle

Vocabulary • Complementary Angles— Two positive angles whose measures have a sum of 90. Angles can be adjacent or nonadjacent.

Vocabulary • Supplementary Angles— Two positive angles whose measures have a sum of 180. Supplementary Angles can be adjacent or nonadjacent.

EXAMPLE 1 In the figure, name a pair of complementary angles, a pair of supplementary angles, and a pair of adjacent angles. R D C A B S T

Example 2 When viewed from the side, the frame of a ballreturn net forms a pair of supplementary angles with the ground. Find m<BCE & m<ECD.

You Try #1 a. Find m<2. b. Find m<3 2 1 4 3

Vocabulary • Linear Pair— two adjacent angles that are supplementary to one another. Noncommon side of each angle are opposite rays.

Vocabulary • Vertical Angles— two angles whose sides form two pairs of opposite rays.

Example 3 Identify all the linear pairs and all the vertical angles in the figure

Example 4 Two angles form a linear pair. The measure of one angle is five times the measure of the other angle. Find the measure of each angle.

Interpreting a Diagram CAN CONCLUDE: • • Adjacent Angles Vertical angles Supplementary angles Point of Intersection Collinear Points Coplanar Points Interior/Exterior Points CANNOT CONCLUDE: • Congruent Segments • Congruent Angles • Complementary Angles

You Try #2 What can you and cannot conclude from the diagram?