The interior angle of a regular polygon is 20°more than three times the exterior angle determine the number of sides of polygon

Answer 1

Let x be the measure of the exterior angle of the polygon.

The interior angle of a regular polygon is 180 - x degrees.

According to the given condition, the interior angle is 20 more than three times the exterior angle, so we have:

180 - x = 3x + 20

Solving for x:

180 - x = 3x + 20
160 = 4x
x = 40

Now that we know the measure of the exterior angle is 40 degrees, we can find the number of sides of the polygon:

n = 360 / x
n = 360 / 40
n = 9

Therefore, the polygon has 9 sides.