Pre-Calculus Homework Solutions 192

# Pre-Calculus Homework Solutions 192 - 55 The smallest angle...

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55. The smallest angle is opposite the side with the smallest measure, 20. Let x and 20 x be the measures of the segments formed by the angle bisector. By the Angle Bisector Theorem, 20 x x ¬ 2 3 4 0 . 20 x x ¬ 2 3 4 0 30 x ¬ 480 24 x 54 x ¬ 480 x ¬ 8 9 0 or 8 8 9 20 x ¬ 10 9 0 or 11 1 9 The segments have measures 8 8 9 and 11 1 9 . 56. By the Exterior Angle Inequality Theorem, m 8 m 6, m 8 m 3 m 4, and m 8 m 2. Thus, the measures of 6, 4, 2, and 3 are all less than m 8. 57. By the Exterior Angle Inequality Theorem, m 1 m 5 and m 1 m 7. Thus, the measures of 5 and 7 are greater than m 1. 58. By the Exterior Angle Inequality Theorem, m 1 m 7 and m 6 m 7. Thus, the measures of 1 and 6 are less than m 7. 59. By the Exterior Angle Inequality Theorem, m 2 m 6, m 7 m 6, and m 8 m 6. Thus, the measures of 2, 7, and 8 are all greater than m 6. 60. y mx b y 2 x 4 61. m 0 8 2 0 8 2 or 4 y mx b y 4 x ( 8) y 4 x 8 62. m 0 1 6 2 6 3 or 2 y y 1 ¬ m ( x x 1 ) y 6 ¬ 2( x 2) y 6 ¬ 2 x 4 y ¬ 2 x 2 63. y y 1 ¬ m ( x x 1 ) y ( 3) ¬ 4[ x ( 2)] y 3 ¬ 4( x 2) y 3 ¬ 4 x 8 y ¬ 4 x 11 64. c 2 ¬ 3 2
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