Question

In the given figure, if $AB||CD,\angle APQ={50}^{\circ }and\angle PRD={127}^{\circ }$, the value of y is:

• A. ${77}^{\circ }$
• B. ${127}^{\circ }$
• C. ${130}^{\circ }$
• D. ${50}^{\circ }$

Answer 1

The correct option is A

${77}^{\circ }$

Given AB and CD are parallel lines. PR is intersecting both parallel lines so it is a transversal.

Then,
$\angle APR=\angle PRD$ [alternate angles]
$\Rightarrow {50}^{\circ }+y={127}^{\circ }$
$\Rightarrow y={77}^{\circ }$