Question

The angles of a quadrilateral are in the ratio $1:2:3:4$. The largest angle is:

• A. ${36}^o$
• B. ${72}^o$
• C. ${108}^o$
• D. ${144}^o$

Answer 1

The correct option is D ${144}^o$

Given ratio of angles of quadrilateral $ABCD$ is $1:2:3:4$.

Let the angles of quadrilateral $ABCD$ be $1x,2x,3x,4x$, respectively.

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

$\Rightarrow 1x+2x+3x+4x={360}^o$

$\Rightarrow 10x={360}^o$

$\therefore x={36}^o$.

$\therefore \angle A=1x=1\times {36}^o={36}^o$,

$\angle B=2x=2\times {36}^o={72}^o$,

$\angle C=3x=3\times {36}^o={108}^o$

and $\angle D=4x=4\times {36}^o={144}^o$.

$\therefore$ The largest angle $={144}^o$.

Hence, option $D$ is correct.