1.5: Describe Angle Pair Relationships 1.6: Classify Polygons Objectives: 1.To use special angle relationships to find angle measures 2.To define, name,

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1.5: Describe Angle Pair Relationships 1.6: Classify Polygons Objectives: 1.To use special angle relationships to find angle measures 2.To define, name, and classify polygons

Vocabulary ComplementarySupplementaryLinear Pair Vertical AnglesPolygonDiagonal (n.) ConvexConcaveEquilateral EquiangularRegular

C Comes Before S…

Example 1a 1.Given that <1 is a complement of <2 and m<1 = 68°, find m<2. 2.Given that <3 is a supplement of <4 and m<3 = 56°, find m<4.

Example 1b 1.What is the sum of complementary angles in radians? 2.What is the sum of supplementary angles in radians? 3.What is complement for the angle that measures π /3? 4.What is the supplement for the angle that measures 3 π /4?

Example 2 Let <A and <B be complementary angles and let m<A = (2x )° and m<B = (x + 10)°. What is (are) the value(s) of x? What are the measures of the angles?

Linear Pairs of Angles

linear pairTwo adjacent angles form a linear pair if their noncommon sides are opposite rays. supplementaryThe angles in a linear pair are supplementary.

Vertical Angles

vertical anglesTwo nonadjacent angles are vertical angles if their sides form two pairs of opposite rays. Vertical angles are formed by two intersecting lines. GSP

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

Example 4: SAT In the figure and, what is the value of x ?