Question

10. The exterior angle of a regular polygon is one-eighth the interior angle. Find the number of sides.
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Answer 1

Answer:

number of sides of the polygon is 160

Step-by-step explanation:

let the interior angle of the regular polygon be x. Therefore, exterior angle of the regular polygon will be 180-x.

according to question ,

180-x=x/8

1440-8x=x

1440=9x

x=1440/9

x=160

Answer 2

Answer

Step-by-step explanation:

Let interior angle be x

Then the exterior angle is x/8

Sum of an interior angle and an exterior angle is 180.

Hence,

x+x/8=180

9x/8=180

therefore,

x=160

Hence, exterior angle is equal to 20 degrees.

Sum of all exterior angles is 360 degrees, and number of sides is equal to number of exterior angles.

Number of sides =  

360/20=18

Hence, number of sides are 18.