Pre-Calculus Homework Solutions 56

Pre-Calculus Homework Solutions 56 - 35 39 Given Prove m 1...

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35. Extend the ray that forms the 157° angle in the opposite direction so that the line crosses the left line of the pair of parallel lines. Then m 4 90. m 5 m 4 m 2 ¬ 180 m 5 ¬ 180 m 4 m 2 m 5 ¬ 180 90 m 2 m 5 ¬ 90 m 2 2 ¬ 3 m 2 ¬ m 3 m 3 157 ¬ 180 m 3 ¬ 23 m 2 ¬ 23 m 1 m 5 ¬ 180 m 1 90 m 2 ¬ 180 m 1 90 23 ¬ 180 m 1 67 ¬ 180 m 1 ¬ 113 36. x ¬ 90 3 y 11 ¬ y 19 3 y ¬ y 30 2 y ¬ 30 y ¬ 15 3 y 11 4 z 2 x ¬ 180 3(15) 11 4 z 2 90 ¬ 180 4 z 126 ¬ 180 4 z ¬ 54 z ¬ 13.5 37. 7 y 4 7 x 9 ¬ 180 7 y 7 x 5 ¬ 180 7 y 7 x ¬ 175 7 y ¬ 175 7 x y ¬ 1 7 (175 7 x ) y ¬ 25 x 2 y 5 11 x 1 ¬ 180 2(25 x ) 5 11 x 1 ¬ 180 50 2 x 5 11 x 1 ¬ 180 54 9 x ¬ 180 9 x ¬ 126 x ¬ 14 y ¬ 25 x ¬ 25 14 or 11 z 7 x 9 ¬ 180 z 7(14) 9 ¬ 180 z 107 ¬ 180 z ¬ 73 38. The angle with measure 40° is congruent to an angle that forms a linear pair with the angle whose measure is x °. So 40 x 180. Then x 140. 39. Given: m Prove: 1 ¬ 8 2 ¬ 7 Proof: 40. Given: m n , is a transversal. Prove: 1 and 2 are supplementary; 3 and 4 are supplementary. Proof: 41. Given: m , m n Prove: n Proof: Since m , we know that 1 2, because perpendicular lines form congruent right angles. Then by the Corresponding Angles Postulate, 1 3 and 2 4. By the definition of congruent angles, m 1 m 2, m 1 m 3 and m 2 m 4. By substitution, m 3 m 4. Because 3 and 4 form a congruent linear pair, they are right angles. By definition,
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