Question

Angles of a quadrilateral are in the ratio $3:6:8:13$. The largest angle is :

• A. ${178}^{\circ }$
• B. ${90}^{\circ }$
• C. ${156}^{\circ }$
• D. ${36}^{\circ }$

Answer 1

The correct option is C ${156}^{\circ }$

Given ratio of angles of quadrilateral $ABCD$ is $3:6:8:13$

Let the angles of quadrilateral $ABCD$ be $3x,6x,8x$,and $13x$, respectively.

We know, by angle sum property, the sum of angles of a quadrilateral is ${360}^o$.

$\Rightarrow 3x+6x+8x+13x={360}^o$

$\Rightarrow 30x={360}^o$
$\Rightarrow x=\frac{{360}^o}{12}$

$\therefore x={12}^o$.

$\therefore \angle A=3x=3\times {12}^o={36}^o$,

$\angle B=6x=6\times {12}^o={72}^o$,

$\angle C=8x=8\times {12}^o={96}^o$

and $\angle D=13x=13\times {12}^o={156}^o$.

$\therefore$ The largest angle $={156}^o$.

Hence, option $C$ is correct.