Question

The ratio of the interior angle of a regular polygon to the exterior angle is 13:2 . How many sides does it have?

Answer 1

15

Explanation:

Int angle : Ext angle : Total

13 : 2 : 15 (13+2)

We know that, int angle + ext angle = 180

Let's introduce a variable x to help solve this ratio

Our ratio is now - 13 x : 2 x : 15x

Use your total ratio and equate it to your total angle size

15 x = 180

x = 180 / 15 = 12

So,

Int angle = 13 x = 13 (12) = 156

Ext angle = 2 x = 2 × 12 = 24

Now, use this formula.

Ext angle = 360 / n

(n represents your number of sides)

24 = 360 / n

n = 360 / 24 = 15