Answer:
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
