To determine the number of sides in a polygon based on the sum of its interior angles, we can use the formula:
(n – 2) × 180 = Sum of interior angles
where n is the number of sides in the polygon. In this case, we know that the sum of the interior angles is 540 degrees. So, we can set up the equation:
(n – 2) × 180 = 540
Next, we divide both sides of the equation by 180:
n – 2 = 540 / 180
n – 2 = 3
Now, we solve for n by adding 2 to both sides:
n = 3 + 2
n = 5
This means that the polygon has 5 sides. Therefore, a polygon with a sum of interior angles equal to 540 degrees is a pentagon.