Question

In the figure, the value of x is ________.

• A. ${20}^{\circ }$
• B. ${10}^{\circ }$
• C. ${15}^{\circ }$
• D. ${25}^{\circ }$

Answer 1

The correct option is A ${20}^{\circ }$


In the given figure, we can see that BE intersects FC at O.
$\therefore$ $\angle BOC=\angle FOE={90}^{\circ }$
(Since they are vertically opposite angles)

Now, AD is a straight line and the sum of the angles on a straight line is ${180}^{\circ }$.

$\Rightarrow \angle AOF+\angle FOE+\angle EOD={180}^{\circ }$
$\Rightarrow x+{90}^{\circ }+3x+{10}^{\circ }={180}^{\circ }$
$\Rightarrow 4x+{100}^{\circ }={180}^{\circ }$
$\Rightarrow 4x={180}^{\circ }-{100}^{\circ }={80}^{\circ }$
$\Rightarrow x=\frac{{80}^{\circ }}{4}={20}^{\circ }$
$\Rightarrow x={20}^{\circ }$