Hey please help me?
2016-05-11 4:06 pm
The difference between the interior and exterior angles of a regular polygon is 132 degree. Find the number of sides of polygon ?
回答 (2)
2016-05-11 4:14 pm
Let n be the number of sides of the polymer.
Exterior angle = 360°/n
Interior angle = 180° - (360°/n)
[180° - (360°/n)] - (360°/n) = 132°
180 - (360/n) - (360/n) = 132°
2(360/n) = 48
n = 2(360)/48
n = 15
The number of sides of polygon = 15
Exterior angle = 360°/n
Interior angle = 180° - (360°/n)
[180° - (360°/n)] - (360°/n) = 132°
180 - (360/n) - (360/n) = 132°
2(360/n) = 48
n = 2(360)/48
n = 15
The number of sides of polygon = 15
2016-05-11 4:25 pm
"The difference between the interior and exterior angles of a regular polygon is 132 degree."
i - e = ±132°
i + e = 180°
-------------
2i = 312°, 48°
i = 156° or 24°
e = 24° or 156°
The exterior angle of a regular n-gon is 360°/n.
There is no n for which 360°/n = 156°, so e≠156°.
e = 24°
360°/15 = 24°
the polygon has 15 sides
i - e = ±132°
i + e = 180°
-------------
2i = 312°, 48°
i = 156° or 24°
e = 24° or 156°
The exterior angle of a regular n-gon is 360°/n.
There is no n for which 360°/n = 156°, so e≠156°.
e = 24°
360°/15 = 24°
the polygon has 15 sides
收錄日期: 2021-05-01 13:11:57
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