Question

The angles of a quadrilateral are in the ratio $3:5:9:13$. Then angles of the quadrilateral respectively are ___________.

• A. ${36}^o,{60}^o,{108}^o,{156}^o$
• B. ${30}^o,{60}^o,{45}^o,{15}^o$
• C. ${45}^o,{20}^o,{30}^o,{60}^o$
• D. ${30}^o,{90}^o,{60}^o,{20}^o$

Answer 1

The correct option is A ${36}^o,{60}^o,{108}^o,{156}^o$

Given ratio of angles of a quadrilateral $ABCD$ is $3:5:9:13$

Let the angles of the quadrilateral $ABCD$ be $3x,5x,9x$ and $13x$, respectively.

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

$\Rightarrow 3x+5x+9x+13x={360}^o$

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

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

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

$\angle B=5x=5\times {12}^o={60}^o$,

$\angle C=9x=9\times {12}^o={108}^o$

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

Hence, option $A$ is correct.