MCQ
In Fig. if $AB$ is parallel to $CD,$ then the value of $\angle \text{BPE}$ is: 
- A$106^\circ$
- B$76^\circ$
- ✓$74^\circ$
- D$84^\circ$
Since, $AB || CD$
$\therefore \angle \text{BPQ}= \angle \text{PQC}$ [Alternate interior angles]
$\Rightarrow(3\text{x}+34)^\circ=(5\text{x}-14)^\circ$
$\Rightarrow 3\text{x}+34=5\text{x}-14$
$\Rightarrow 48=2\text{x}$
$\Rightarrow \text{x}=24$
$\therefore \angle\text{BPQ}=(3\times 24+34)^\circ=106^\circ$
$\angle \text{BPQ}+\angle \text{BPE}=180^\circ$ [EF is a straight line]
$\Rightarrow 106^\circ+\angle \text{BPE}=180^\circ$
$\Rightarrow \angle \text{BPE}=74^\circ$
Hence, the correct answer is option $(c).$
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