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1-5: Exploring Angle Pairs Types of Angle Pairs • Adjacent angles are two angles with a common side, common vertex, and no common interior points (next to). • Vertical angles are two angles whose sides are opposite rays (across from). Types of Angle Pairs, con’t • Complementary angles are two angles whose measures have a sum of 90. – Each angle is the complement of the other. • Supplementary angles are two angles whose measures have a sum of 180. – Each angle is the supplement of the other. Identifying Angle Pairs • Using the diagram, decide whether each statement is true. – BFD and CFD are adjacent angles. – AFB and EFD are vertical angles. – AFE and BFC are complementary. – AFE and CFD are vertical angles. – DFE and BFC are supplementary. – AFB and BFD are adjacent. Making Conclusions from a Diagram • Using the diagram, which angles can you conclude are… …congruent? …vertical angles? …adjacent angles? …supplementary angles? Making Conclusions From a Diagram • Using the diagram, can you conclude the following: TW WV ? PW WQ? TWQ is a right angle? TV bisects PQ? Linear Pairs • A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays. – The angles of a linear pair form a straight line. Linear Pair Postulate: If two angles form a linear pair, then they are supplementary. Finding Missing Angle Measures • KPL and JPL are a linear pair, mKPL = 2x + 24, and mJPL = 4x + 36. • What are the measure of KPL and JPL? ABC and DBC are a linear pair. mABC = 3x + 19 and mDBC = 7x – 9. What are the measures of ABC and DBC? Angle Bisectors • An angle bisector is a ray that divides an angle into two congruent angles. • Its endpoint is at the angle vertex. Using an Angle Bisector • AC bisects DAB. If mDAC = 58, what is mDAB?