Question

If the internal angle of an equal polygon is 1500, then tell the number of its sides? (A). 10 (B). 12 (C). 15 (D). 18​

Answer 1

The question seems error, so it is changed.

Question:

If the sum of the interior angles of a regular polygon is 1800°, then what is the number of its sides?

(A). 10

(B). 12

(C). 15

(D). 18

Solution:

We know that the sum of the interior angles of an 'n' sided regular polygon is,

(n - 2)180°

Using this, we find the no. of sides of the regular polygon.

Given that the sum of the interior angles of the regular polygon is 1800°.

(n - 2)180° = 1800°

=> n - 2 = 1800° / 180°

=> n - 2 = 10

=> n = 10 + 2

=> n = 12

Hence it's a 12 sided regular polygon. So option (B) is the answer.

Let's check.

One exterior angle of a 12 sided regular polygon = 360° / 12 = 30°

Hence one interior angle = 180° - 30° = 150°

So the sum of interior angles = 150° × 12 = 1800°

Hence checked!!!