The angles of a quadrilateral are in the ratio in the ratio 2 : 5 : 7 : 4. The largest angle is:

1. 40°

2. 100°

3. 140°

4. 80°

As we know, the sum of all the angles in a quadrilateral is 360°.

The angles are in the ratio 2 : 5 : 7 : 4.

Let x be the common factor. Therefore, the angles are 2x, 5x, 7x and 4x.

⇒ 2x + 5x + 7x + 4x = 360°

⇒ 18x = 360°

⇒ x = $\dfrac{360°}{18}$

⇒ x = 20°

The angles are:

2x = 2 $\times$ 20° = 40°
5x = 5 $\times$ 20° = 100°
7x = 7 $\times$ 20° = 140° (Largest angle)
4x = 4 $\times$ 20° = 80°

Hence, option 3 is the correct option.