The angle 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 A

Given:  

Ratio of angles of quadrilateral 2:5:7:10 

Formula Used: 

Sum of angles of quadrilateral = $$360\degree$$​​

Solution:

\$$\text{Sum of angles of the quadrilateral:} \\2x + 5x + 7x + 10x = 360 \\\text{Simplify the sum:} \\24x = 360 \\\text{Solve for } x: \\x = \frac{360}{24} = 15 \\\text{Calculate individual angles:} \\\text{Smallest angle: } 2x = 2 \times 15 = 30^\circ \\\text{Next angle: } 5x = 5 \times 15 = 75^\circ \\\text{Next angle: } 7x = 7 \times 15 = 105^\circ \\\text{Largest angle: } 10x = 10 \times 15 = 150^\circ \\\text{Difference between the greatest and smallest angles:} \\ 150^\circ - 30^\circ = 120^\circ$$​​