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

1. 54°

2. 135°

3. 162°

4. 108°

According to the properties of polygons, if a polygon has n sides, then the sum of its interior angles is (2n - 4) x 90°.

A pentagon have 5 sides.

Sum of its interior angles = (2 x 5 - 4) x 90°

= (10 - 4) x 90°

= 6 x 90°

= 540°.

It is given that the interior angles of the pentagon are in the ratio 2 : 5 : 6 : 4 : 3.

So,

⇒ 2a + 5a + 6a + 4a + 3a = 540°

⇒ 20a = 540°

⇒ a = $\dfrac{540°}{20}$

⇒ a = 27°

The angles are:

⇒ 2a = 2 x 27° = 54°

⇒ 5a = 5 x 27° = 135°

⇒ 6a = 6 x 27° = 162°

⇒ 4a = 4 x 27° = 108°

⇒ 3a = 3 x 27° = 81°

Thus, the largest angle = 162°.

Hence, option 3 is the correct option.