Question

Pls answer this question!!!!

The ratio of exterior angle to the interior angle of a regular polygon is 1 : 14 respectively. Find the number of sides of the polygon.

Answer 1

No of sides is 30 sides it means the polygon is called as tricontagon

Answer 2

${Answer :-}$

Ratio of interior angle to exterior angle is 14:1.
Let, interior angle be 14x and exterior be x.
So, 14x + x = 180.
Or, 15x = 180.
Or, x = 12.

Thus, interior angle of the polygon is 14 * 12 = 168 degree.

Let n be the number of sides of the polygon.

Now, by condition, we have,
Or, 168 = ( n-2) *180/n
Or, 168n = 180n - 360
Or, 180n - 168n = 360
Or, 12n = 360.
Or, n = 360/12 = 30.

Hence, number of sides of the polygon is 30.

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