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

∴2n−4n×90∘=150∘⇒2n−4n=15090=53

By cross multiplication:

6n−12=5n⇒6n−5n=12⇒n=12

∴ Number of sides of polygon is 12.

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

∴2n−4n×90∘=150∘⇒2n−4n=15090=53

By cross multiplication:

6n−12=5n⇒6n−5n=12⇒n=12

∴ Number of sides of polygon is 12.

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