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標題:
f.2 簡單pentagon
發問:
it is given that an interior angle of a regular n-gon is 36 more than its exterior angle a:find the size of an exterior angle of the regular n-gon b:find the value of n
最佳解答:
Interior angle = (n - 2) X 180* / n Exterior angle = 360* / n So, for an interior angle is larger than the exterior angle by 36*, (n - 2)(180*)/n = 360*/n + 36* 180*n - 360* = 360* + 36*n 144*n = 720* n = 5 Exterior angle = 360* / 5 = 120* So, the n-gon is a pentagon, with 5 sides. 2010-05-17 09:14:09 補充： Sorry, exterior angle = 360*/5 = 72*
其他解答:
An alternative method : a. Let yo be the exterior angle. Then, the interior angle = (y + 36)o y + (y + 36) = 180 y = 72 Exterior angle = 72o b. n = 360/72 = 5
f.2 簡單pentagon
發問:
it is given that an interior angle of a regular n-gon is 36 more than its exterior angle a:find the size of an exterior angle of the regular n-gon b:find the value of n
最佳解答:
Interior angle = (n - 2) X 180* / n Exterior angle = 360* / n So, for an interior angle is larger than the exterior angle by 36*, (n - 2)(180*)/n = 360*/n + 36* 180*n - 360* = 360* + 36*n 144*n = 720* n = 5 Exterior angle = 360* / 5 = 120* So, the n-gon is a pentagon, with 5 sides. 2010-05-17 09:14:09 補充： Sorry, exterior angle = 360*/5 = 72*
其他解答:
An alternative method : a. Let yo be the exterior angle. Then, the interior angle = (y + 36)o y + (y + 36) = 180 y = 72 Exterior angle = 72o b. n = 360/72 = 5
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