Question

An irregular polygon has exterior angle measures of 92, 73, 63, and 104 degrees. What is the measure of the fifth interior angle?

Answer 1

the exterior angles of a polygon is 360°

92 + 73 + 63 + 104 = 332

360 - 332 = 28° is the measure of the fifth interior angle.

Answer 2

152°

Explanation:

the sum of the exterior angles of a polygon = 360°

let x be the measure of the fifth exterior angle , then

92° + 73° + 63° + 104° + x = 360°

332° + x = 360° ( subtract 332° from both sides )

x = 28°

then

interior angle + exterior angle = 180° , that is

interior angle + 28° = 180° ( subtract 28° from both sides )

interior angle = 152°