The ratio between the interior angle and the exterior angle of a regular polygon is 2:1,
Find :
1.Each exterior angle of this polygon.
2.Number of sides in the polygon.
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Answer:
If the ratio of each exterior angle to each interior angle is 2:3, then then ratio of the sum of the exterior angles to the sum of the interior angles is also 2:3
Be careful, the sum of the interior angles of a polygon is actually (n-2)×180, but I'm going to use (180n-360):
3/2=(180n-360)/360
3/2=½n-1
5/2=½n
5=n
We should double check that a pentagon IS the correct polygon
An exterior angle on a regular pentagon is 360/5=72
An interior angle on a regular pentagon is 180-72=108
72/108=2/3
72:108=2:3
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