Question

How many sides does a regular polygon have if each of its interior angle is 168°??

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Answer 1

Answer:

Any polygon have only 5 sides.

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Answer 2

Answer:

Let the sides be n.

Then sum of all interior angles of n-sided polygon = (n - 2) × 180°

So each interior angle of regular n-sided polygon = (n - 2) × 180° ÷ n

=> 168 = (n - 2) × 180 ÷ n

=> n - 2 = 168n/180

=> 180n/180 - 168n/180 = 2

=> 12n/180 = 2

=> 12n = 360

=> n = 30

Therefore this regular polygon has 30 sides.

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