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## Find Measures of Angles

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**Find Measures of Angles**In the figure, m|| n and t is a transversal. If m7 = 123°, find m2 and m8. Since 7 and 2 are alternate exterior angles, they are congruent. So, m2 = 123°. Answer:m2 = 123° Since 7 and 8 are corresponding angles, they are congruent. So, m8 = 123°. Answer:m8 = 123°**In the figure, m|| n and t is a transversal. If m4 =**57°, find m5 and m1. A.m5 = 57°; m1 = 57° B.m5 = 123°; m1 = 123° C.m5 = 57°; m1 = 123° D.m5 = 123°; m1 = 57°**LEG LIFTSKian does leg lifts each morning. For each**repetition he lifts his legs 35 degrees off the ground. What is the measure of the angle formed by his body and legs in this position? The angles are supplementary. x + 35 = 180 Write the equation. x = 180 – 35 Subtract 35 from each side. x = 145 Answer: The angle formed by his body and legs is 145°.**SEWING Linda cuts a piece of material from the corner at a**35° angle. What is the measure of the other angle formed by the cut? A. 145° B. 90° C. 55° D. 35° 90 - 35**Find Measures of Angles**ALGEBRAAngles PQR and STU are supplementary. If mPQR = x – 15 and mSTU = x – 65, find the measure of each angle. Step 1 Find the value of x. Step 2 Replace x with 130 to find the measure of each angle. x – 15 + x – 65 = 180° 2x – 80 = 180° 2x = 260° x = 130° x – 15 = 130 – 15 or 115 x – 65 = 130 – 65 or 65 Answer:mPQR = 115° mSTU = 65°**Angles ABC and DEF are complementary. If mABC = x + 12**and mDEF = 2x – 9, find the measure of each angle. A.mABC = 29°; mDEF = 61° B.mABC = 41°; mDEF = 49° C.mABC = 59°; mDEF = 121° D.mABC = 71°; mDEF = 109°**TRANSPORTATIONA road crosses railroad tracks at an angle as**shown. If m1 = 131°, find m6 and m5. Since 1 and 5 are corresponding angles, they are congruent. Answer:m5 = 131° Since 5 and 6 are supplementary angles, the sum of their measures is 180°.180 – 131 = 49 Answer:m6 = 49°**TRANSPORTATION Main Street crosses Broadway Boulevard and**Maple Avenue at an angle as shown. If m1 = 48°, find m3 and m4. A.m3 = 132°; m4 = 48° B.m3 = 48°; m4 = 132° C.m3 = 48°; m4 = 42° D.m3 = 42°; m4 = 138°