Question

Find the value of x in the figure.

• A. ${30}^{\circ }$
• B. ${40}^{\circ }$
• C. ${50}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is C

${50}^{\circ }$

In $△BEG$,
$\angle 1=\angle GBE+\angle BGE$
(Exterior angle property of a triangle)
$\Rightarrow \angle 1={40}^{\circ }+{65}^{\circ }$
$\Rightarrow \angle 1={105}^{\circ }$

Now, $\angle 2=\angle BGE$
(Since vertically opposite angles are equal)
$\Rightarrow \angle 2={65}^{\circ }$

Similarly $\angle GFC=\angle AFD={90}^{\circ }$

Now, in $△FGC$
$\angle 2+\angle 3+{90}^{\circ }={180}^{\circ }$
$\Rightarrow \angle 3={180}^{\circ }-{90}^{\circ }-{65}^{\circ }$
$\Rightarrow \angle 3={25}^{\circ }$

Now, in $△AEC$
$x+\angle 1+\angle 3={180}^{\circ }$
$\Rightarrow x+{105}^{\circ }+{25}^{\circ }={180}^{\circ }$
$\Rightarrow x={180}^{\circ }-({105}^{\circ }+{25}^{\circ })$
$\Rightarrow x={50}^{\circ }$