Question

ABCD is a parallelogram. Points P and Q are taken on the sides AB and AD respectively and the parallelogram PRQA is formed, If $\angle C={40}^{\circ }$, find $\angle R$ and $\angle P$

Answer 1

As opposite sides of a parallelogram are parallel

$\Rightarrow AD\parallel BC$

also $AQ\parallel PR$

$\Rightarrow AD\parallel PR$

$\Rightarrow BC\parallel PR$

Similarly $QR\parallel DC\Rightarrow \angle PRQ=\angle BCD={40}^o$

$AP\parallel QR\Rightarrow \angle APR+\angle PRQ={180}^o$ ( Internal angles)

$\Rightarrow \angle APR={140}^o$

$\angle R={40}^o,\angle P={140}^o$