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

Explanation

Given: A polygon whose exterior and interior angles are in the ratio `1:5`.
We know that the sum of one exterior angle and one interior angle is `180°` as they form a linear pair.
Now let's say that the exterior angle is x.
And it is given that the interior angle is in the ratio `1:5`.
`∴` The interior angle measure will be `5x`
Now,
`⇒x+5x=180°`
`6x=180^@`
`x=30°`
Now, the sum of exterior angle in polygon `=360°`
Let the number of sides be `n`.
`∴n×x=360°`
`n×30°=360°`
`n=12`
`∴`Hence, the number of sides are of polygon are `12`.