Question

The ratio of exterior angle to interior angle of a regular polygon is 1:4. Find the number of sides of the polygon.

Answer 1

Let the interior angle of the regular polygon be x.
Therefore, the exterior angle is x/4.

Exterior angle + adjacent interior angle = 180°
x/4 + x. = 180°
5x /4. = 180°
x. = 180° * 4/5
= 144°

The interior angle is 144°.
The exterior angle is 36°.

Let n be the number of sides.

n = 360°/ exterior angle
= 360° / 36°
= 10

Ans.= The number of sides of a regular polygon is 10.

Answer 2

Ratio of exterior angle : interior angle = 1 : 4

Let x be the constant ratio

Ratio of exterior angle : interior angle = 1x : 4x

Solve x:

Sum of adjacent angles on a straight line is 180°

x + 4x = 180

5x = 180

x = 36°

Find one exterior angle:

exterior angle = x = 36°

Find the number of sides:

Sum of all exterior angles add up to 360°

Number of sides = 360 ÷ 36 = 10

Answer: It is a 10-sided polygon