To find the number of sides of a polygon when you have the interior angle sum, you can use the formula:
Interior Angle Sum = (n – 2) × 180
Here, n represents the number of sides in the polygon. Rearranging the formula to solve for n, we get:
n = (Interior Angle Sum / 180) + 2
So, if you know the interior angle sum, simply divide it by 180, add 2 to that quotient, and you’ll find the number of sides. For example, if the interior angle sum is 540 degrees:
n = (540 / 180) + 2 = 3 + 2 = 5
This means the polygon is a pentagon, which has 5 sides. Remember that this method applies only to simple polygons, where the sides do not intersect each other.