Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1:5.
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
By cross multiplication:
∴ Number of sides of polygon is 12.