Question

Ques.45:- The interior angle of a regular polygon is 156°. Find the number of sides of the regular polygon-
(a) 12 ( )
(b) 13 ( )
(c) 14 ( )
(d) 15 ( )

which option is true??​

and solve it step-by-step

Answer 1

Answer:

(d) 15

Step-by-step explanation:

Sum of all the interior angles add up to (n - 2) x 180 where n is the number of sides.

Given that an angle is 156°, and there are n sides.

Sum of all the interior angles will be 156n.

Solve n:

156n = (n - 2) x180

156n = 180n - 360

24n = 360

n = 15

Answer: (d) 15

Answer 2

Answer:

Step by step:-

Given data

-let the number of sides of a polygon be x

formula for each interior angle = {( 2n-4)*90}/n}

156 *n=(2n-4)*90

156=180n -360

=156-180=-360

=-24=-360

n=-360/24

ANS:- 15

option D} 15 is correct