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
f.2 簡單pentagon
2010-05-17 6:17 am
回答 (2)
2010-05-17 7:37 am
✔ 最佳答案
Interior angle = (n - 2) X 180* / nExterior 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*
參考: Prof. Physics
2010-05-17 12:27 pm
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
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
收錄日期: 2021-04-19 22:15:55
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