Question

$AB||CD,\angle APQ={50}^o,\angle PRD={177}^o$ find $x$ and $y$ ?

Answer 1

Here, $AB\parallel CD$

$\therefore \angle APQ={50}^o=\angle PQR[AlternateinterioranglesforAB\parallel CD,PQistransversal]$

i.e. $x={50}^o$

Again,

$\angle PRD={127}^o=\angle APR[AlternateinterioranglesforAB\parallel CD,PRistransversal]$

And, $\angle APR=\angle APQ+\angle QPR\Rightarrow {127}^o={50}^o+\angle QPR\Rightarrow \angle QPR={127}^o-{50}^o={77}^o$

i.e. $y={77}^o$

$\therefore x={50}^o,y={77}^o.$