Question

If interior angles of a pentagon are in the ratio 1:2:3:4:5, find the measure of smallest angle

Answer 1

Answer:

Step-by-step explanation:

Let the interior angles be x, 2x, 3x, 4x and 5x.

The formula for finding the sum of the measure of the interior angles is (n - 2) * 180.

We know that sum of all interior angles of a pentagon = (5 - 2)*180 = 540°

=> x +2x + 3x + 4x + 5x = 540

=> 15x = 540

=> x = 540/15 = 36°.

Thus the angles are 36°, 72°, 108°, 144°, 180°.

The smallest angle is 36°