Question

calculate the number of sides of a regular polygon whose each interior angle is 160 degree

Answer 1

We have two ways to find the number of sides:

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METHOD 1: INTERIOR ANGLES

Sum of all interior angles = ( n - 2) x 180 where n is the number of sides

⇒ one angle = [  ( n - 2) x 180  ] ÷ n

Find n, the number of sides:

Given that one interior angle is 160

[  ( n - 2) x 180  ] ÷ n  = 160

(n - 2) x 180  = 160n

n - 2 = 8/9 n

n - 8/9 n = 2

1/9 n = 2

n = 2 x 9

n = 18

Answer: There are 18 sides

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METHOD 2: EXTERIOR ANGLES

Sum of exterior angles = 360º

Find one exterior angle:

Interior angle + exterior angle = 180 { the two angles form a straight line)

160 + exterior angle = 180

exterior angle = 180 - 160 = 20º

Find number of sides:

Number of sides = 360 ÷ 20 = 18

Answer: There are 18 sides.

Answer 2

Given that,
Each exterior angle of the polygon = 160°
We know that the sum of exterior angles of each polygon is 360°
Now we will find the exterior angle of the polygon.
180°-160°=20° (Linear pair)
Therefore, each exterior angle of the polygon=20°
Now, Number of sides of the polygon
= 360÷20 =18
Therefore, the polygon have 18 sides.


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