Question

A pentagon has four of its angles equal. If the

size of the fifth angle is 60°, find the size of each
of the four equal angles.

Answer 1

120 degrees

Explanation:

The sum of the interior angles of a pentagon is given by the formula, where S is the sum of the interior angles, and n is the number of sides of the polygon:

S = (n - 2) × 180 degrees

For a pentagon, n = 5, so we have:

S = (5 - 2) × 180 = 540 degrees

If four of the angles are equal, we can let x be the measure of each of those angles. Then, we can write an equation for the sum of the angles:

4x + 60 = 540

Solving for x, we get:

4x = 540 - 60 = 480

x = 480/4 = 120

Therefore, each of the four equal angles in the pentagon has a measure of 120 degrees.