If the interior angles of a pentagon are in the ratio 1 : 3 : 5 : 7 : 11, then the measure of the smallest interior angle is:

Correct option is B

Given:

The interior angles of a pentagon are in the ratio 1 : 3 : 5 : 7 : 11.

Concept Used:

The sum of the interior angles of a polygon with n sides is given by the formula (n - 2) $$\times$$​ 180°.

A pentagon has 5 sides.

Solution:

Calculate the sum of the interior angles of a pentagon:(5 - 2) $$\times$$​180° = 3 $$\times$$ 180° = 540°​

Let the angles be x, 3x, 5x, 7x, and 11x.

x + 3x + 5x + 7x + 11x = 540°

27x = 540°

x =$$\frac{540° }{ 27}$$​​

x = 20°

The smallest interior angle is x, which is 20°.

Therefore, the measure of the smallest interior angle is 20°.