The interior angles of a regular pentagon each measure:

## The reasoning A regular pentagon has 5 equal sides and 5 equal angles. Here's the principle: **The sum of interior angles of any polygon = (n − 2) × 180°**, where n is the number of sides. For a pentagon: n = 5 Sum of interior angles = (5 − 2) × 180° = 3 × 180° = **540°** Since it's *regular*, all 5 angles are equal: Each angle = 540° ÷ 5 = **108°** ## Why the wrong options tempt you **120°** — This is each interior angle of a regular *hexagon* (6 sides). Students mix up their polygons! **144°** — This is for a regular *decagon* (10 sides). Way too many sides. **150°** — This is for a regular *dodecagon* (12 sides). The pattern tricks you because the numbers seem close. The trap: memorizing random angles instead of understanding the formula. When you forget which angle belongs to which shape, you'll pick wrongly. ## Quick takeaway **Pentagon = 5 sides → (5−2)×180° = 540° → divide by 5 = 108°.** Master the formula, and you'll handle *any* polygon they throw at you!