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An exterior angle of a regular polygon is one-third of its interior angle. How many sides does the polygon have?

  • A.6
  • B.8
  • C.9
  • D.10

Answer: B

Let the exterior angle be x. The interior angle is 3x.

The sum of an interior and its corresponding exterior angle is 180°.

x + 3x = 180°

4x = 180°

x = 45°.

The exterior angle is 45°. The number of sides n = 360° / 45° = 8.

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