Question

Find the value of x in the given figure.

Answer 1

$\angle BAC+\angle BAE={180}^{\circ }$
(Since both the angles form a linear pair of angles)

$\Rightarrow \angle BAC+{110}^{\circ }={180}^{\circ }$
$\Rightarrow \angle BAC={70}^{\circ }$

Now, $\angle ABC+\angle BAC=\angle ACD$
(Since, exterior angle of a triangle is equal to the sum of its two opposite interior angles)

$\Rightarrow x+{70}^{\circ }={120}^{\circ }$

$\Rightarrow x={50}^{\circ }$