Question

In the given figure, if AB || CD || EF,
PQ || RS, $\angle RQD=25°\text{and}\angle CQP=60°$, then find $\angle QRS$ .

• A. 145°
• B. 135°
• C. 130°
• D. 140°

Answer 1

The correct option is A 145°

Given AB || CD, RQ is the transversal.
$\angle RQD=\angle ARQ=25°$ (Alternate interior angles)

Given PQ||RS, RQ is the transversal.
Then, $\angle SRB=\angle PQC=60°$ (Alternate exterior angles).

$\angle ARS+\angle SRB=180°$ (Linear pair)
$\Rightarrow \angle ARS+60°=180°$
$\Rightarrow \angle ARS=120°$

$\angle QRS=\angle ARS+\angle ARQ$
$\Rightarrow \angle QRS=120°+25°=145°$