If the angles of a pentagon sum up to 540 degrees, what is the measure of each angle if they are equal?

To determine the measure of each angle in a regular pentagon, where all angles are equal, we start with the known fact that the sum of the interior angles of a polygon can be calculated using the formula ( (n - 2) \times 180 ), where ( n ) is the number of sides.

For a pentagon, ( n = 5 ). Plugging in the values, we have:

[ (5 - 2) \times 180 = 3 \times 180 = 540 \text{ degrees} ]

This tells us that the total sum of the interior angles of a pentagon is indeed 540 degrees, confirming the setup of the problem.

If all five angles in the pentagon are equal, we can find the measure of each angle by dividing the total sum of the angles by the number of angles:

[ \frac{540 \text{ degrees}}{5} = 108 \text{ degrees} ]

Thus, each angle in a regular pentagon measures 108 degrees, which matches the provided choice. This is the reason why this answer is correct; it accurately applies the geometry of polygons and the calculations necessary to find the measures of the angles in a