Which of the following is not an exterior angle of a regular polygon?

Analyze the question: A regular polygon with n sides has equal exterior angles, each equal to 360°/n. So an angle can be an exterior angle of a regular polygon only if 360° divided by that angle gives a whole number (the number of sides).

Concept: n = 360° ÷ exterior angle, and n must be a whole number (n ≥ 3).

Check each option:

• A. 66°: 360 ÷ 66 = 5.4545... → not a whole number ✗
• B. 72°: 360 ÷ 72 = 5 → a regular pentagon ✓
• C. 24°: 360 ÷ 24 = 15 → a regular 15-sided polygon ✓
• D. 15°: 360 ÷ 15 = 24 → a regular 24-sided polygon ✓

Answer: Only 66° fails to give a whole number of sides, so it is not an exterior angle of a regular polygon.

Tip: For "which cannot be an exterior angle" questions, divide 360 by each option. If the result is not a whole number, that is your answer. The angle must be a factor of 360.