Lines and Angles — MATHS STD 7 — Question

Construction: Draw a line $PQ$ parallel to $AB$ which is also parallel to $CD$
Since, $PQ || CD$
$\therefore \angle \text{EFC}=\angle \text{FEQ}=37^\circ$ [Alternate angles]
Now, $\angle \text{AEQ}+\angle \text{FEQ}=\angle \text{AEF}$
$\Rightarrow \angle \text{AEQ}+37^\circ=95^\circ$
$\Rightarrow \angle \text{AEQ}=58^\circ$
Since, $PQ || AB$
$\therefore \angle \text{EAB}+\angle \text{AEQ}=180^\circ$ [Angles on the same side of a transversal line are supplementary]
$\Rightarrow \angle\text{EAB}+58^\circ=180^\circ$
$\Rightarrow \angle\text{EAB}=122^\circ$
$\angle\text{EAB}+\text{Reflex}\angle\text{EAB}=360^\circ$ [Complete angle]
$\therefore 122^\circ+(2\text{x})^\circ=360^\circ$
$\Rightarrow 2\text{x}=238$
$\Rightarrow \text{x}=119$
Hence, the correct answer is option $(d).$