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

JAMB Mathematics 2023 55 views

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

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

Explanation

Interior and exterior angles of any polygon are supplementary, meaning they add up to 180 degrees. Let x represent the exterior angle. The interior angle is 5x. Set up equation: x plus 5x equals 180.

Solve: 6x equals 180, so x equals 30 degrees. The exterior angle is 30 degrees. For regular polygons, the sum of all exterior angles always equals 360 degrees.

Divide 360 by the exterior angle to find the number of sides: 360 divided by 30 equals 12 sides. A polygon with 12 sides is called a dodecagon. A hendecagon has 11 sides, enneadecagon has 19, and icosagon has 20.

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