Question

Four exterior angles of a pentagon measure 20°, 81°, 33°, and 152°. What is the measure of the of the fifth exterior angle?

Answer 1

74 degrees because the exterior angles of a polygon always add up to 360%

Answer 2

The measure of the fifth exterior angle is 74°

Explanation:

To find the measure of the exterior angle of a polygon we need to know that;

The sum of the exterior angle of a polygon is 360° .

That is, if we add up all the exterior angle of a polygon, it is going to give us a total of 360° .

So in this question we have been given the measure of four of the exterior angle and we are asked to find the fifth exterior angle.

Let x be the measure of the fifth exterior angle.

20° + 81° + 33° + 152° + x = 360°

286° + x = 360°

To get the value of x, we will subtract 286 from both-side of the equation;

286° + x - 286° = 360° - 286°

(At the left-hand side of the equation, 286° will cancel-out -286° leaving us with just x, and the right-hand side of the equation 286° will be subtracted from 360°)

x = 360° - 286°

x = 74°

Therefore the measure of the fifth exterior angle is 74°.