Question

If the angles of a quadrilateral are in the ratio 13 : 14 : 15 : 18

The difference between the greatest and the smallest angle is

• A. ${30}^{\circ }$
• B. ${78}^{\circ }$
• C. ${108}^{\circ }$
• D. ${20}^{\circ }$

Answer 1

The correct option is A

${30}^{\circ }$

Let the angles be $13x,14x,15x,and18x$

$\because$ Sum of interior angles of a quadrilateral $={360}^{\circ }$

$\Rightarrow 13x+14x+15x+18x={360}^{\circ }$

$\Rightarrow 60x={360}^{\circ }$

$\Rightarrow x=\frac{{360}^{\circ }}{60}$

$\Rightarrow x=6^{\circ }$

$\therefore Theanglesare$

$13x=13\times 6={78}^{\circ }$

$14x=14\times 6={84}^{\circ }$

$15x=15\times 6={90}^{\circ }$

$18x=18\times 6={108}^{\circ }$

$\therefore {78}^{\circ }isthesmallestangleand{108}^{\circ }isthegreatest.$

$\text{The difference between the greatest and the smallest angle is}$

$={108}^{\circ }-{78}^{\circ }={30}^{\circ }$