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Section 1.6 Angle Pair Relationships standard #13 5/3/2017 Goals • Vertical Angles and Linear Pairs • Complementary and Supplementary Angles Vertical Angles 2 angles whose sides form two pairs of opposite rays. These angles are congruent and lie on opposite sides of the point of intersection. <1 & <2 are vertical. m<1 ≅ m< 2. 3 1 2 4 <3 & <4 are vertical. m<3 ≅ m<4. Linear Pair • Two adjacent angles whose non-common sides are opposite rays. The angles will add up to 180°. The angles lie on the same line. 1 2 m<1 + m<2 = 180° Complementary Angles • Two angles that add to 90°. Each angle is the complement of the other. However, these angles do not have to be adjacent in order to be complementary. 1 2 m<1 + m<2 = 90° Supplementary Angles • Two angles that add to 180°. Each angle is the supplement of the other. However, these angles do not have to be adjacent in order to be supplementary. m<1 + m<2 = 180° 1 2 Example #1 A. Are 1 and 2 a linear pair? Yes B. Are 4 and 5 a linear pair? No, No, <3≠<5 C. Are 5 and 3 vertical angles?<4+<5≠180° D. Are 1 and 3 vertical angles? Yes 2 3 1 5 4 Example #2 • In one town, Main Street and Columbus Avenue intersect to form an angle of 36°. Find the measures of the other three angles. 1 36 2 3 Answers to #2 1) m<1 = 144° 2) m<2 = 36° (180-36) (Vertical Angles are congruent) 3) m<3 = 144° (Vertical Angles are congruent) 1 36 ° 2 3 Example #3 Solve for x and y. Then find the angle measures. 4x+15 5x+30 3y+15 3y-15 Answers to #3 1) 2) 3) 4) X 4x + 15 + 5x + 30 = 180° 9x + 45 = 180° 9x = 135° x = 15 Y 1) 2) 3) 3y + 15 + 3y - 15 = 180° 6y = 180° y = 30 Example #4 A. Given that G is a supplement of H and mG is 82°, find mH. B. Given that U is a complement of V, and mU is 73°, find mV. Answers to #4 1) 82° + mH = 180° 2) mH = 98° 1) 73° + mV = 90° 2) mV = 17° Assignment Page 47 #8-32 66-71