Question

In the given figure, if AB || CD and EF || DQ, then $\angle PDQ$ is .............

• A. ${48}^{\circ }$
• B. ${34}^{\circ }$
• C. ${72}^{\circ }$
• D. ${68}^{\circ }$

Answer 1

The correct option is D ${68}^{\circ }$

Given : $AB||CD;EF||DQ$

To find : $\angle PDQ$

$\because AB||CD$ and $PE$ is transversal

$\angle PDC$ and $\angle PEA$ are corresponding angles.

$\therefore PEA={34}^{\circ }$

$\angle PEA+\angle PEF+\angle FEB={180}^{\circ }$ (Linear pair)

${34}^{\circ }+\angle PEF+\angle FEB={180}^{\circ }$

$\angle PEF={180}^{\circ }-{34}^{\circ }-{78}^{\circ }$

$\angle PEF={68}^{\circ }$

$\because EF||DQ$

$\angle PDQ=\angle PEF={68}^{\circ }$

$\therefore \angle PDQ={68}^{\circ }$