Question

For the given figure, $\angle JBH={120}^o$ and the vertical lines are parallel.
Find the angle $\angle HAK.$

• A. ${90}^o$
• B. ${60}^o$
• C. ${180}^o-{120}^o$
• D. ${30}^o$

Answer 1

Answer: (B), (C)

${180}^o-{120}^o$

In the given figure, HG is the transversal.

Hence, $\angle HAK$ and $\angle HBI$ are corresponding angles.

As KL and IJ are parallel, corresponding angles are equal in measure.
$\therefore \angle HAK=\angle HBI$

Also, $\angle JBI$ is a straight angle.
$\therefore \angle JBI={180}^o$
Also, from the figure, $\angle JBI=\angle JBH+\angle HBI$
Substituting this in the above equation,
$\angle JBH+\angle HBI={180}^o$
$\Rightarrow \angle HBI={180}^o-\angle JBH={180}^o-{120}^o={60}^o\Rightarrow \angle HAK=\angle HBI-{60}^o$