L.T. I can identify special angle pairs and use their relationships to find angle measure.

A. Vertical Angles Previously, you learned that two angles are adjacent if they share a common vertex and side but have no common interior points. In this lesson, you will study other relationships between pairs of angles.  1 and  3 are vertical angles.  2 and  4 are vertical angles Two angles are vertical angles if their sides form two pairs of opposite rays. Vertical Angle Pairs are CONGRUENT

B. Linear Pairs  5 and  6 are a linear pair. 5 6 Two adjacent angles are a linear pair if the form a straight line. Linear Angle Pairs add up to 180°. 30 ° 150°

Finding Angle Measures In the stair railing shown,  6 has a measure of 130˚. Find the measures of the other three angles. SOLUTION  6 and  8 are vertical angles. So, they are congruent and have the same measure. m  8 = m  6 = 130˚ °  6 and  7 are a linear pair. So, the sum of their measures is 180˚. m  6 + m  7 = 180˚ 130˚ + m  7 = 180˚ m  7 = 50˚  7 and  5 are vertical angles. So, they are congruent and have the same measure ° 130° All 4 angles together equal 360°

Definition: Two angles are supplementary if the sum of their measures is 180 degrees. Each angle is the supplement of the other. 1 2 These are supplements of each other because their angles add up to 180. C. Supplementary Angles

Example 1 Find the value of x.

Example 2 Find the value of x.

Example 3 Find the value of x.

Definition: Two angles are complementary if the sum of their measures is 90 degrees. Each angle is the complement of the other. 1 2 These are complements of each other because their angles add up to be 90. D. Complementary Angles

Example 4 Find the value of x.

Example 5 Find the value of x.

Definition: An angle bisector is a ray that divides an angle into two congruent angles. It cuts the angle in half. E. Angle Bisector