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Question

Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1:5.
 


Solution

Ratio in exterior angle and interior angles of a regular polygon = 1:5
But sum of interior and exterior angles = 180 (Linear pair)
Exterior angle = 180×11+5=180×16=30
and interior angles = 180×56=150
Let number of sides of the polygon = n 
2n4n×90=1502n4n=15090=53
By cross multiplication:
6n12=5n6n5n=12n=12 
Number of sides of polygon is 12.

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