The problem asks which of the given angles (66°, 72°, 24°, 15°) is not an exterior angle of a regular polygon. The sum of the exterior angles of any polygon is 360°. In a regular polygon, all exterior angles are equal. Therefore, an exterior angle of a regular polygon must be a factor of 360.

1. Problem Description

The problem asks which of the given angles (66°, 72°, 24°, 15°) is not an exterior angle of a regular polygon. The sum of the exterior angles of any polygon is 360°. In a regular polygon, all exterior angles are equal. Therefore, an exterior angle of a regular polygon must be a factor of

3

6

0.

2. Solution Steps

To determine which angle is not an exterior angle of a regular polygon, we need to check if 360 is divisible by each of the given angles.

* Check 66°: $360 / 66 = 5.4545...$. Since the result is not an integer, 66° is not an exterior angle of a regular polygon.

* Check 72°: $360 / 72 = 5$. Since the result is an integer, 72° is an exterior angle of a regular polygon (pentagon).

* Check 24°: $360 / 24 = 15$. Since the result is an integer, 24° is an exterior angle of a regular polygon (15-gon).

* Check 15°: $360 / 15 = 24$. Since the result is an integer, 15° is an exterior angle of a regular polygon (24-gon).

Therefore, 66° is the only angle that is not an exterior angle of a regular polygon.

3. Final Answer

A. 66°