1.6 Angle Pair Relationships

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1.6 Angle Pair Relationships

Which angles are adjacent? <1&<2, <2&<3, <3&<4, <4&<1 Then what do we call <1&<3? Vertical Angles – 2 angles that share a common vertex & whose sides form 2 pairs of opposite rays. <1&<3, <2&<4 2 1 3 4

Linear Pair (of angles) 2 adjacent angles whose non-common sides are opposite rays. 1 2

Example Vertical angles? <1 & <4 Adjacent angles? <1&<2, <2&<3, <3&<4, <4&<5, <5&<1 Linear pair? <5&<4, <1&<5 Adjacent angles not a linear pair? <1&<2, <2&<3, <3&<4 2 1 3 5 4

Important Facts Vertical Angles are congruent. The sum of the measures of the angles in a linear pair is 180o.

Example: If m<5=130o, find m<3 m<6 m<4 4 =130o =50o 5 3 6

Example: Find x y m<ABE m<ABD m<DBC m<EBC x=40 y=35 3x+5o y+20o B x+15o 4y-15o D C x=40 y=35 m<ABE=125o m<ABD=55o m<DBC=125o m<EBC=55o

Complementary Angles 2 angles whose sum is 90o 1 2 55o A <1 & <2 are complementary <A & <B are complementary B

Supplementary Angles 2 angles whose sum is 180o <1 & <2 are supplementary. <X & <Y are supplementary. 1 2 130o 50o X Y

Ex: <A & <B are supplementary. m<A is 5 times m<B Ex: <A & <B are supplementary. m<A is 5 times m<B. Find m<A & m<B. m<A + m<B = 180o m<A = 5(m<B) Now substitute! 5(m<B) + m<B = 180o 6(m<B)=180o m<B=30o m<A=150o