Question

In th figure, for which value of x is $l_1\left|\right|l_2$?

Answer 1

In the figure, $l_1\left|\right|l_2$

$\therefore \angle EBA=\angle BAH$ (Alternate angles)

$\therefore \angle BAH={78}^{\circ }$

$\Rightarrow \angle BAC+\angle CAH={78}^{\circ }$

$\Rightarrow \angle BAC+{35}^{\circ }={78}^{\circ }$

$\Rightarrow \angle BAC+{78}^{\circ }-{35}^{\circ }={43}^{\circ }$

In $\Delta ABC,\angle C={90}^{\circ }$

$\therefore \angle ABC+\angle BAC={90}^{\circ }$

$\Rightarrow x+{43}^{\circ }={90}^{\circ }\Rightarrow x={90}^{\circ }-{43}^{\circ }$

$\therefore x={47}^{\circ }$