Question

calculate the no.of sides of a regular polygon if the interior angle is 5times its exterior​

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

Let the exterior angle be 'x'.

Given that Each interior angle is 5 times the exterior angle.

We know that exterior angle + interior adjacent angle = 180

⇒ x + 5x = 180

⇒ 6x = 180

⇒ x = 180/60

⇒ x = 30.

Now,

We know that sum of exterior angles of any polygon = 360.

⇒ Number of sides n = (360/exterior angle)

⇒ n = (360/x)

⇒ n = (360/30)

⇒ n = 12.

Therefore, the number of sides = 12.

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