Question

A polygon has an interior angle that is five times larger than its exterior angle. How many sides does the polygon have?

Answer 1

• The polygon has 12 sides

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We know the sum of a pair of interior and exterior angles is 180°.

Let the exterior angle be x then we have:

• x + 5x = 180
• 6x = 180
• x = 30

We also know that sum of all exterior angles is 360°.

If the number of sides is n, then we have:

• 30n = 360
• n = 360/30
• n = 12