Question

The values of $x$ and $y$ are
(a) $x=130,y=120$
(b) $x=120,y=130$
(c) $x=120,y=120$
(d) $x=130,y=130$

Answer 1

In figure, In $△ABD$

$\angle BAD={59}^{\circ },\angle BDA={61}^{\circ }$ are the interior angles.

$\angle DBC=y^{\circ }$ is an exterior angle of the $△ABD$.

Since,

In a triangle, exterior angle is equal to sum of its opposite interior angles.

$\Rightarrow y^{\circ }={61}^{\circ }+{59}^{\circ }$

$\Rightarrow y^{\circ }={120}^{\circ }$

$\Rightarrow y=120$---(1)

In figure, $\angle ADB=\angle GDE={61}^{\circ }$ [Since, Vertically opposite angles]

Now, In $△GDE$,

$\angle DGE={69}^{\circ },\angle GDE={61}^{\circ }$are the interior angles.

$\angle GEF=x^{\circ }$ is an exterior angle of the $△GDE$

Since, In a triangle, exterior angle is equal to sum of its opposite interior angles.

$\Rightarrow x^{\circ }={61}^{\circ }+{69}^{\circ }$

$\Rightarrow x^{\circ }={130}^{\circ }$

$\Rightarrow x=130$---(2)

From (1) and (2), $x=130,y=120$

Hence, the correct answer is option (a).