Question

Construct a parallelogram $PQRS$, given $PQ=5$ cm, $QR=4$ cm and $\angle PQR={70}^o$ and calculate $\angle QRS$.

• A. ${90}^o$
• B. ${105}^o$
• C. ${110}^o$
• D. None of these

Answer 1

The correct option is C ${110}^o$

$\Rightarrow$ We know that opposite sides and angle of parallelogram are equal.

$\Rightarrow$ And adjacent angles of parallelogram are supplementary. By using these properties we are going to construct a parallelogram.

$\Rightarrow$ Draw a line segment $PQ=5cm$

$\Rightarrow$ Construct an angle of ${70}^{\circ }$ at point $Q$.

$\Rightarrow$ Cut off $QR=4cm$

$\Rightarrow$ Construct an angle of ${110}^{\circ }$ at point $P$.

$\Rightarrow$ Cut off $PS=4cm$

$\Rightarrow$ Join $RS$

$\Rightarrow$ Thus $PQRS$ is a required parallelogram

We have to measure an $\angle QRS$

$\Rightarrow$ $\angle QRS={110}^{\circ }$