1. Section 1-5: Exploring Angle Pairs Objectives: Identify special angle pairs & use their relationships to find angle measures.

2. Vertical Angles Two angles whose sides are opposite rays. Adjacent Angles Two coplanar angles with a common side, a common vertex, and no common interior points Complementary Angles Two angles whose measures have the sum of 90. Each angle is called the complement of the other. Supplementary Angles Two angles whose measures have the sum of 180. Each angle is called the supplement of the other. FOUR TYPES OF ANGLE PAIRS

3. Name all pairs of angles in the diagram that are: a.vertical b.supplementary Two angles are supplementary if the sum of their measures is 180. A straight angle has measure 180, and each pair of adjacent angles in the diagram forms a straight angle. So these pairs of angles are supplementary: Vertical angles are two angles whose sides are opposite rays. Because all the angles shown are formed by two intersecting lines,  1 and  3 are vertical angles, and  2 and  4 are vertical angles.  1 and  2,  2 and  3,  3 and  4, and  4 and  1. Identify the Angle Pairs c.complementary Two angles are complementary if the sum of their measures is 90. No pair of angles is complementary.

4. Draw Conclusions from a Diagram You can conclude that angles are: Adjacent Angles Adjacent supplementary angles Vertical angles Cannot conclude from a diagram unless there are markings: Angles and segments are  An angle is a right angle Lines are parallel or perpendicular

5. Although  3 appears to be a right angle, it is not marked with a right angle symbol, so you cannot conclude that  3 is a right angle. You can conclude that  1 and  5 are adjacent because they share a common side, a common vertex, and no common interior points.  3 and  5 are not marked as congruent on the diagram. Although they are opposite each other, they are not vertical angles. So you cannot conclude that  3   5. Angle Pairs Use the diagram below. Which of the following can you conclude:  3 is a right angle,  1 and  5 are adjacent,  3   5?

6. Postulates & Definitions Recall that a linear pair is a pair of adjacent angles that form a straight angle. LINEAR PAIR POSTULATE: If two angles form a linear pair, then they are supplementary. An angle bisector is a ray that divides one angle into two angles with the same measure.

7. Problem Reason 2x + 24 + 4x +36 = 180 Linear Pair Postulate 6x + 60 = 180 Simplify 6x = 120 Subtraction Property of Equality x =20 Division Property of Equality Find Missing Angle Measures