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

Given the measure of each interior angle of a regular polygon is five times the measure of its exterior angle.

Each interior angle of a regular polygon =180°(n-2)/n

Each exterior angle of a regular polygon = 360°/n

According to question,

180°(n-2)/n = 5 × 360°/n

36(n-2) = 360

n-2=10

n=12

Number of sides of the polygon =12

Answer 2

Answer:

• 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