Question

In Fig $6.23$, if $AB\parallel CD,\angle APQ={50}^o$ and $\angle PRB={127}^o$, find $a$ and $y$

Answer 1

As $AB\parallel CD$ and $PQ$ is transversal.

$\therefore \angle APQ=\angle PQR\left(\text{Alternate interior angles}\right)$

$\Rightarrow 50°=a$

Also,

$\angle APR=\angle PRD\left(\text{Alternate interior angles}\right)$

$\Rightarrow 50°+\angle QPR=127°$

$\Rightarrow y=127°-50=77°$