Question

In a quadrilateral $PQRS,\angle P,\angle Q,\angle R$ and $\angle S$ are interior angles. If $\angle P:\angle Q:\angle R:\angle S=1:2:3:4$, then which angle is equal to ${144}^{\circ }$.

• A. $\angle P$
• B. $\angle Q$
• C. $\angle R$
• D. $\angle S$

Answer 1

The correct option is D $\angle S$

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

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

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

$\Rightarrow 1x+2x+3x+4x={360}^o$
$\Rightarrow 10x={360}^o$

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

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

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

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

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

$\therefore$ $\angle S={144}^o$.

Hence, option $D$ is correct.