Question

Question 126

Find the value of x in the given figure.

Answer 1

In the given figure, $\angle BAC={80}^{\circ },\angle ABC={30}^{\circ },\angle ACE=x$ and $\angle ECD={90}^{\circ }$
In $\Delta ABC$, we know that, exterior angle is equal to the sum of interior opposite angles.
$\therefore$ $\angle ACD=\angle CAB+\angle ABC$
$\Rightarrow \angle ACE+\angle ECD={80}^{\circ }+{30}^{\circ }$ $[\because \angle ACD=\angle ACE+\angle ECD]$
$\Rightarrow \angle ACE+{90}^{\circ }={110}^{\circ }$ $[\because \angle ECD={90}^{\circ }]$
$\Rightarrow \angle ACE=x={110}^{\circ }-{90}^{\circ }={20}^{\circ }$