Question

State true or false:

In quadrilateral PQRS, $\angle P:\angle Q:\angle R:\angle S=3:4:6:7$

Is PS also parallel to QR?

• A. True
• B. False

Answer 1

The correct option is B False

Given in $\square$ PQRS,$\angle P:\angle Q:\angle R:\angle S=3:4:6:7$

Let $\angle P=3x,\angle Q=4x,\angle R=6x,\angle S=7x$

Sum of interior angles of a quadrilateral$={360}^o$

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

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

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

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

$\Rightarrow x={18}^o$

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

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

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

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

In quadrilateral PQRS, $\angle P\&\angle Q$ are not supplementary

as well as $\angle S\&\angle R$ are not supplementary.

So QR is not parallel to SP.