Question

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

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Answer 1

Answer:

If the interior angle is 3x, the exterior angle is x. Hence 3x+x = 4x = 180 or x = 45. The interior angle is 135 deg. So the polygon has 360/45 = 8 sides or it is a regular octagon.

Step-by-step explanation:

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Answer 2

Answer:

8 , which is an octagon

Step-by-step explanation:

Let the interior angle be x . Then ,exterior angle is 1/3x .

interior angle = 180 - exterior

So , x = 180 -1/3x

x = interior angle = 135°

exterior angle = 1.3 x = 1/3 *135 = 45°

Exterior angle = 360 /n

45 = 360 /n

n = 360 /45

  = 8 sides

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