The Triangles and Its Properties — MATHS STD 7 — Question

In $\triangle \text{ABD}$
$\angle \text{ADB}+\angle \text{BAD}+\angle \text{ABD}=180^\circ$ [Angle sum property of triangle]
$\Rightarrow 61^\circ+59^\circ+\angle \text{ABD}=180^\circ$
$\Rightarrow \angle \text{ABD}=60^\circ$
$\angle \text{ABD}+\angle \text{DBC}=180^\circ$ [Linear pair angles]
$\Rightarrow 60^\circ+\text{y}^\circ=180^\circ$
$\Rightarrow \text{y}=120$
Now, $\angle \text{ADB}=\angle \text{GDE}=61^\circ$ [Vertically opposite angles]
Now, In $\triangle \text{GDE},$
$\angle \text{GDE}+\angle \text{DGE}+\angle \text{GED}=180^\circ$ [Angle sum property of triangle]
$\Rightarrow 61^\circ+69^\circ+\angle \text{GED}=180^\circ$
$\Rightarrow \angle \text{GED}=50^\circ$
Now, $\angle \text{GED}+\angle \text{GEF}=180^\circ$ [Linear pair angles]
$\Rightarrow 50^\circ+\text{x}^\circ=180^\circ$
$\Rightarrow \text{x}=130$
Hence, the correct answer is option $(a).$