Question

From the given figure, find the value of x.

Answer 1

In $\Delta ABC,\angle CAB+\angle ABC+\angle BCA={180}^{\circ }$ [angle sum property of a triangle]
$\Rightarrow {25}^{\circ }+{35}^{\circ }+\angle BCA={180}^{\circ }\Rightarrow \angle BCA={180}^{\circ }-{60}^{\circ }\Rightarrow \angle BCA={120}^{\circ }$
Also, $\angle BCA$ is an exterior angle
$\therefore \angle BCA=\angle D+y$
$\Rightarrow y=\angle BCA-\angle D={120}^{\circ }-{60}^{\circ }$ $[\because \angle D={60}^{\circ },given]$
$\Rightarrow y={60}^{\circ }$
Now, $\angle x$ and $\angle y$ form a linear pair
$\therefore x+y={180}^{\circ }\Rightarrow x+{60}^{\circ }={180}^{\circ }\Rightarrow x={180}^{\circ }-{60}^{\circ }={120}^{\circ }$