Question

If $AB$ $||$ $CD$, $\angle APQ$ $={50}^o$ and $\angle$ $PRD$ $={127}^o$, then $x$ and $y$ respectively are ___________.

• A. ${40}^o,{30}^o$
• B. ${50}^o,{77}^o$
• C. ${30}^o,{45}^o$
• D. ${90}^o,{30}^o$

Answer 1

The correct option is B ${50}^o,{77}^o$

$\angle x=\angle APQ$ ($\because AB||CD$, as given in question)

$x={50}^{\circ }$

$\angle PRQ=180-\angle PRD\Rightarrow \angle PRQ=180-127={53}^{\circ }$

$\therefore y=180-x-\angle PRQ\Rightarrow y=180-50-53\Rightarrow y={77}^{\circ }$