Question

If four of the exterior angles of a convex pentagon measure

59°, find the measure of the fifth exterior angle.
O137°
O None of these answers are correct.
154°
124°
114⁰

Answer 1

The measure of the fifth exterior angle of a convex pentagon, with the other four angles being 59° each, is calculated to be 124°.

Step-by-step explanation:

The sum of the exterior angles of any polygon is 360°.

Since four of the exterior angles of a convex pentagon are known to be 59° each, to find the measure of the fifth exterior angle, we can subtract the sum of the known exterior angles from 360°:

Sum of known exterior angles = 4 × 59° = 236°

Measure of the fifth exterior angle = 360° - 236° = 124°

Therefore, the measure of the fifth exterior angle of the convex pentagon is 124°.