For a regular polygon, the sum of the interior angles is 250% more than the sum of its exterior angles. Each interior angle of the polygon measures x°. What is the value of x?

Correct option is A

Given:

The sum of the interior angles is 250% more than the sum of its exterior angles.

Each interior angle of the polygon measures x$$^\circ.$$​​

Formula Used:

Sum of exterior angles of any polygon = 360°.

Sum of interior angles of a polygon with ( n ) sides =180 (n - 2).

Interior angle of a regular polygon =$$\frac{180(n-2)}{n}$$​​

Solution:

Let the number of sides of the polygon be n.

The sum of the exterior angles is always 360°, and the sum of the interior angles is 180 (n - 2).

According to the problem, the sum of the interior angles is 250% more than the sum of the exterior angles. This means:
180(n-2) = 360 + 2.5$$\times 36$$​0
180(n - 2) = 360 + 900 = 1260

180(n - 2) = 1260
n - $$2 = \frac{1260}{180} = 7$$​​
n = 9

The number of sides is 9. Now, we calculate each interior angle:
x =$$\frac{180(n-2)}{n} = \frac{180(9-2)}{9} = \frac{180 \times 7}{9} = 140^\circ$$​​

Thus, each interior angle of the polygon is 1$$40^\circ.$$​​