Four interior angles of a pentagon measure 88°, 118, 132, and 100°. What is the measure of the fifth interior angle?

82

92

102

112

fifth angle = 102°

Step-by-step explanation:

A pentagon is a polygon that have 5 sides. A pentagon can be divided into 3 triangles. And the sum of angle in a triangle is 180°. Therefore the sum of interior angle in a pentagon will be 180 * 3 = 540°. The sum of interior angles of a pentagon = 540°.

The general rule for calculating sum of the interior angles of a polygon is

sum of interior angle = (n-2) * 180°

where

n = number of sides

n = 5 since we are dealing with a pentagon.

sum of interior angle of a pentagon = 540°

The fifth angle can be computed when you subtract the sum of the 4 angles from 540°.

fifth angle = 540 - (88 + 118 + 132 + 100)

fifth angle = 540 - 438

fifth angle = 102°