Question

In the figure, if $AB\parallel CD,\angle APQ={50}^{}$ and $\angle PRD={127}^{}$, find $x$ and $y$.

Answer 1

Given, $AB\parallel CD,\angle APQ={50}^{\circ },\angle PRD={127}^{\circ }$
According to the question

$x={50}^{\circ }$ (Alternate interior angles.)

$\angle PRD+\angle RPB={180}^{\circ }$ (Angles on the same side of transversal.)

$\Rightarrow {127}^{\circ }+\angle RPB={180}^{\circ }$

$\Rightarrow \angle RPB={53}^{\circ }$

Now, $y+{50}^{\circ }+\angle RPB={180}^{\circ }$ ($AB$ is a straight line.)

$\Rightarrow y+{50}^{\circ }+{53}^{\circ }={180}^{\circ }$

$\Rightarrow y+{103}^{\circ }={180}^{\circ }$

$\Rightarrow y={77}^{\circ }$

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