Question

9. Find the number of sides of a regular polygon if each of its interior angle is168°.​

Answer 1

Answer:

No. of sides of a regular polygon=n

Each interior angle=168°

each exterior angle=180-168=12°no.of sides of regular polygon=360/each exterior angle

=360/12

=30sides

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Answer 2

Number of sides of a polygon be n.

Sum of interior angles of regular polygon = (n - 2)*180

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

Given

Each interior angles of regular polygon = 168 degrees

(n - 2)*180/n = 168

(n - 2)/n = 168/180

1 - (2/n) = 168/180

2/n = 1 - 168/180

2/n = (180 - 168)/180

2/n = 12/180

1/n = 6/180

1/n = 1/30

n = 30

Therefore number of sides of a given polygon are 30. ——> Answer.