The size of each interior angle of a regular polygon is 8 times the size of
each exterior angle.
Work out how many sides the polygon has.
Let the size of each exterior angle be x degrees in your working.

The polygon has 18 sides

Step-by-step explanation:

In this question, we are tasked with calculating the number of sides in a polygon given that the size of each interior angle is 8 times the size of each exterior angle.

We were told that the size of each exterior angle is x . This means the size of each interior angle which is 8 times would be 8x

mathematically, for a polygon, the sum of the interior angles is (n-2)180 = 180n - 360

Now for each of the interior angles, the size we have will be [180n-360]/n and this is equal to 8x

Hence [180n-360]/n = 8x

or simply x = [180n-360]/8n

For the exterior angle, the sum of the exterior angle in a polygon is 360. The value of each exterior angle of a polygon of n side would be 360/n

Now this value is equal to x ;

x = 360/n

since we have two x now, we equate both to each other.

360/n = [180n -360]/8n

we can cancel the n on both denominator sides

360 = (180n-360)/8

180n - 360 = 8 * 360

180n = (8 * 360) + 360

180n = (9 * 360)

n = (9 * 360)/180

n = 9 * 2

n = 18