Question

State true or false:

In quadrilateral PQRS, $\angle P:\angle Q:\angle R:\angle S=3:4:6:7$. The smallest angle of the quadrilateral is ${45}^o$.

• A. True
• B. False

Answer 1

The correct option is B False

Given ratio of angles of quadrilateral $PQRS$ is $3:4:6:7$

Let the angles of quadrilateral $PQRS$ be $3x,4x,6x,7x$, respectively.

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

$\Rightarrow \angle P+\angle Q+\angle R+\angle S={360}^o$

$\Rightarrow 3x+4x+6x+7x={360}^o$

$\Rightarrow 20x={360}^o$

$\Rightarrow x=\frac{{360}^o}{20}$

$\therefore x={18}^o$.

$\therefore \angle P=3x=3\times {18}^o={54}^o$,

$\angle Q=4x=4\times {18}^o={72}^o$,

$\angle R=6x=6\times {18}^o={108}^o$

and $\angle S=7x=7\times {18}^o={126}^o$.

$\therefore$ The smallest angle $={54}^o$.

That is, the statement is false.

Hence, option $B$ is correct.