Question

The angles of a pentagon are in the ratio 2 : 5 : 6 : 4 : 3. The largest angle is ______.

पर्याय

• 54°

• 135°

• 162°

• 108°

Answer 1

The angles of a pentagon are in the ratio 2 : 5 : 6 : 4 : 3. The largest angle is 162°.

Explanation:

The sum of the interior angles of a pentagon is given by (5 − 2) × 180° = 540°. Given that the angles are in the ratio 2 : 5 : 6 : 4 : 3, let the angles be 2x, 5x, 6x, 4x, and 3x. Setting up the sum gives:

2x + 5x + 6x + 4x + 3x = 540°

20x = 540°

x = 27°

The largest angle corresponds to the ratio part 6:

Largest angle = 6 × 27° = 162°