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1-5: Exploring Angle Pairs Types of Angle Pairs • Adjacent Angles Two coplanar angles with a: common side ________________, common vertex _______________, _______________________________ no common interior points 1 2 3 4 • Vertical Angles Two angles whose sides are __________ opposite ______ rays 1 3 2 4 B • Complementary Angles Two angles whose measures have a sum 90 of _______ 47 1 2 A • Supplementary Angles Two angles whose measures have a sum 180 of _______ 3 4 43 Example 1: Use the diagram below. Is each statement true? Explain. L M P 74 A 106 O N a. PAL and LAM are adjacent angles. Yes, they have a common side b. PAO and NAM are vertical angles. No, they don’t share two pairs of opposite rays c. PAO and NAO are supplementary. Yes, the sum of the angles is 180° Assumptions About Angles • Assumptions you can make: 1. Angles are adjacent 2. Angles are adjacent and supplementary 3. Angles are vertical angles • Assumptions you can’t make: 1. Angles or segments are congruent 2. An angle is a right angle 3. Angles are complementary Postulate 1-9: Linear Pair Postulate A Linear Pair of angles are angles that are both supplementary and adjacent. Ex 2 What are the measures of ABC and DBC ? C 3 x 19 7 x 9 180 10 x 10 180 10 x 170 x 17 3 x 19 A 7x 9 B D mABC 3(17) 19 70 mDBC 7(17) 9 110 Theorem 2-1: Vertical Angle Theorem Vertical angles are congruent 1 3 and 2 4 1 2 4 3 Example 3: What is the value of x? What are the angle measures? 2 x 42 3 x 10 (2 x 42) (3 x 10) 2 x 52 3 x 52 x 2(52) 42 146 3(52) 10 146 Angle Bisector two • A ________ which divides an angle into ______ ray _______________ angles. congruent X AY is an angle bisector. A Y Z Example 4: LM bisects JLN . If mJLM 42, what is mJLN ? J 2(42) 84 42 L M N Homework: p. 38 # 7-23, 27-32