Question

determine the angle of side of a polygon whose exterior and interior angle are in the ratio 1:5.

Answer 1

Polygon whose exterior and inerior angle are in the ratio 1:5. 
⇒ 360° / (2n - 4) x 90° = 1 / 5 
⇒ 4 / (2n - 4) = 1 / 5 
⇒ 20 = (2n - 4) 
⇒ 2n = 24 
∴ n = 12.

Answer 2

Ratio of exterior angle : interior angle = 1 : 5

Define x:

Let x be the constant ratio

exterior angle : interior angle = 1x : 5x

Solve x:

The sum of the exterior and interior angles is 180º.

1x + 5x = 180

6x = 180

x = 30º

Find the number of sides:

The sum of all exterior angles of a polygon is 360º

Number of sides = 360 ÷ 30 = 12

Answer: This is a 12-sided polygon