Question

the ratio between exterior angle and interior angle of regular polygon is 1:5. find the number of sides of the polygon

Answer 1

The interior angle and the exterior angle always add up to 180.

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Find exterior angle:

exterior angle : interior angle = 1 : 5

1 + 5 = 6

6 parts = 180

1 part = 180 ÷ 6 = 30

exterior angle = 30°

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Find number of sides:

Since we know that sum of all exterior angles of a polygon = 360°

Number of sides = 360 ÷ 30 = 12

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Answer: This is a 12 sided polygon.