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Question
The ratio between an exterior angle and an interior angle of a regular polygon is 2 : 3. Find the number of sides in the polygon.
Solution
Let the measure each interior and exterior angles are 3k and 2k.
Let the number of sides of the polygon is n.
Now we can write:
n.3k = ( 2n - 4 ) x 90°
3nk = ( 2n - 4 ) 90° ....(1)
Again
n.2k = 360°
nk = 180°
From (1)
3.180° = ( 2n - 4 ) 90°
3 = n - 2
n = 5
Thus the number of sides of the polygon is 5.
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