Question

In a figure $AB\parallel CD\angle ={35}^o$ and $\angle QRD={135}^o$ find $\angle PQR$.

Answer 1

Draw a line LM parallel to AB passing through point Q

Now, $\angle PQM={35}^o\left(AlternateInteriorAngle\right)$

Also, We know that Adjacent Angles are Supplementary

So, $\angle MQR+{135}^o={180}^o\Rightarrow \angle MQR={45}^o$

Hence, $\angle PQR={35}^o+{45}^o={80}^o$