Question

In figure, if lines $l$ and $m$ are parallel, then the value of $x$, is

Answer 1

Given : $l||m$ and $\angle 2={90}^{\circ }$

From figure, $\angle 1$ and $\angle 2$ form a linear pair.
$\therefore \angle 1+\angle 2={180}^{\circ }$
$\angle 1+{90}^{\circ }={180}^{\circ }$
$\angle 1={90}^{\circ }$

In a triangle, the exterior angle is equal to the sum of the opposite interior angles.
In $△AOB$,
$x+\angle 1={125}^{\circ }$
$x={125}^{\circ }-\angle 1$
$x={125}^{\circ }-{90}^{\circ }$
$x={35}^{\circ }$

Hence, option (a) is correct.