If each interior angle of a regular polygon measures 144°, how many sides does the polygon possess?
Answer and explanation
Correct answer: A. 10 sides
- Step 1: Interior and exterior angles are supplementary: Exterior angle = 180° - 144° = 36°. Step 2. The sum of exterior angles of any convex polygon is 360°. Step 3. Number of sides n = 360° / (exterior angle) = 360° / 36° = 10 sides (decagon). Answer: 10 sides. Why not the others: 8 sides (octagon) has exterior angle 45° and interior 135°; 12 sides has interior 150°; 9 sides has exterior 40°.
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