Pre-Calculus Homework Solutions 240

# Pre-Calculus Homework Solutions 240 - 43 Since n 5 the sum...

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43. Since n 5 5, the sum of the measures of the interior angles is 180(5 2 2) or 540. A regular pentagon has 5 congruent interior angles. Let the measure of one of these angles be x . 540 5 5 x 108 5 x The measure of each interior angle of the Pentagon is 108. Since each interior angle and its corresponding exterior angle form a linear pair, the measure of the exterior angle is 180 2 108 or 72. 44. Yes; both the dome and the architectural elements are based upon a regular octagon. Since n 5 8, the sum of the measures of the interior angles is 180(8 2 2) or 1080. A regular octagon has 8 congruent interior angles. Let the measure of one of these angles be x. 1080 5 8 x 135 5 x The measure of each interior angle is 135. Since each interior angle and its corresponding exterior angle form a linear pair, the measure of the exterior angle is about 180 2 135 or 45. 45. } 180( n n 2 2) } 5 } 180 n n 2 360 } 5 } 180 n n } 2 } 3 n 60 } 5 180 2 } 3 n 60 } The two formulas are equivalent. 46.
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