The interior angle of a regular polygon is nine times the size of its exterior angle. Identify the polygon.

JAMB Mathematics 2024 280 views
Source: JAMB · 2024

The interior angle of a regular polygon is nine times the size of its exterior angle. Identify the polygon.

  1. hendecagon
  2. dodecagon
  3. enneadecagon
  4. icosagon ✓
Explanation

Interior and exterior angles on one side add up to 180°. If interior = 9 × exterior, then 10 × exterior = 180°, so exterior = 18°.

Number of sides = 360° ÷ 18° = 20. A 20-sided polygon is an icosagon.

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