The angles of a quadrilateral are in the ratio 2:5:7:10. Find the difference between the greatest and the smallest angles of the quadrilateral.

Correct option is B

​Given:

Angles ratio = 2:5:7:10

Formula Used:

​$$\text{Sum of angles in a quadrilateral} = 360^\circ$$​ 

​$$\text{Each angle} = \frac{\text{Ratio of angle}}{\text{Sum of ratios}} \times 360$$​​

Solution:

Sum of ratios = 2 + 5 + 7 + 10 = 24 

Now, from the formula;

​$$\text{Smallest angle} = \frac{2}{24} \times 360 = 30^\circ$$​

​$$\text{Greatest angle} = \frac{10}{24} \times 360 = 150^\circ$$​​

​$$Difference=150^∘−30^∘=120^∘.$$ 

Thus, the difference between the smallest and greatest angle is 120 degree.