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Adjacent, Vertical, Supplementary, and Complementary Angles Angles that are “side by side” and share a common ray are called? Adjacent angles 15º 45º These are examples of what type of angles? adjacent angles. 80º 45º 35º 55º 130º 85º 20º 50º These angles are examples of? Non- Adjacent 100º 50º 35º 35º 55º 45º When 2 lines intersect, they make what type of angles? vertical angles 75º 105º 105º 75º What type of angles are opposite one another? Vertical angles 75º 105º 105º 75º Vertical angles are opposite one another. What is the measure of angle A? 75º A 105º 75º Vertical angles are? congruent (equal). 150º 30º 30º 150º Supplementary angles add up to? 180º 40º 120º 60º Adjacent and Supplementary Angles 140º Supplementary Angles but not Adjacent Complementary angles add up to 90º. 30º 40º 50º 60º Adjacent and Complementary Angles Complementary Angles but not Adjacent Angles Around a Point Angles around a point will always add up to 360 degrees. The angles above all add to 360° 53° + 80° + 140° + 87° = 360° Practice Time! Directions: Identify each pair of angles as vertical, supplementary, complementary, or none of the above. #1 120º 60º #1 120º 60º Supplementary Angles #2 30º 60º #2 30º 60º Complementary Angles #3 75º 75º #3 Vertical Angles 75º 75º #4 40º 60º #4 40º 60º None of the above #5 60º 60º #5 60º 60º Vertical Angles #6 135º 45º #6 135º 45º Supplementary Angles #7 25º 65º #7 25º 65º Complementary Angles #8 90º 50º #8 90º 50º None of the above Now, think of what we talked about today. 1 5 2 4 3 Are angles 4 and 5 supplementary angles? no Are angles 2 and 3 complementary angles? no Are angles 4 and 3 supplementary angles? yes Are angles 2 and 1 complementary angles? yes Name the adjacent angles and linear pair of angles in the given figure: Adjacent angles: ABD and DBC A ABE and DBA 00 30 30 Linear pair of angles: EBA, ABC EBD, DBC 0 0 9090 E D 0 60 600 B C Name the vertically opposite angles and adjacent angles in the given figure: C A P B D Vertically opposite angles: APC and BPD Adjacent angles: APC and CPD APB and CPD APB and BPD Pairs Of Angles Formed by a Transversal • Corresponding angles • Alternate angles • Interior angles Corresponding Angles When two parallel lines are cut by a transversal, pairs of corresponding angles are formed. L Line L GPB = PQE G A D P B Q E F Line M Line N GPA = PQD BPQ = EQF APQ = DQF Four pairs of corresponding angles are formed. Corresponding pairs of angles are congruent. Alternate Angles Alternate angles are formed on opposite sides of the transversal and at different intersecting points. L G A D Line L P B Q E Line M Line N BPQ = DQP APQ = EQP F Two pairs of alternate angles are formed. Pairs of alternate angles are congruent. Interior Angles The angles that lie in the area between the two parallel lines that are cut by a transversal, are called interior angles. L G A 120 Line L 0P 600 E Line N APQ + DQP = 1800 1200 600 D B Line M BPQ + EQP = 1800 Q F interior eachside pairofadd AThe pairmeasures of interiorofangles lieangles on the in same theup to 1800. transversal. Name the pairs of the following angles formed by a transversal. GG G AA 500 Line Line Line LL L P P BBB 1300 D DD Q Q Q EEE FFF Line Line Line MM M Line Line N Line NN Directions: Determine the missing angle. #1 ?º 45º #1 135º 45º #2 ?º 65º #2 25º 65º #3 ?º 35º #3 35º 35º #4 ?º 50º #4 130º 50º Find the value of x. x x + 15 = 90 x = 75 15 #5 ?º 140º #5 140º 140º Find the value of x. (4x + 3) (x - 8) (4x + 3) + (x - 8) = 90 5x - 5 = 90 5x = 95 x = 19 #6 ?º 40º #6 50º 40º