# If the sum of the interior angles of a polygon is 540 degrees, then how many sides does the polygon have?

5, 6, 7, 8

**Solution:**

Sum of interior angles of a polygon with n sides = (n - 2) × 180°

Sum of interior angles of a polygon = 540°

Equating both we can determine the number of sides

(n - 2) × 180° = 540°

By further calculation

n - 2 = 540/180

n - 2 = 3

So we get

n = 3 + 2 = 5

Therefore, the polygon has 5 sides and it is a pentagon.

## If the sum of the interior angles of a polygon is 540 degrees, then how many sides does the polygon have?

5, 6, 7, 8

**Summary:**

If the sum of the interior angles of a polygon is 540 degrees, the polygon has 5 sides.