Question

In the given figure, $AB$ $||$ $CD$ $||$ $EF$ and $GH$ $||$ $KL$. Find $x$.

• A. ${85}^o$
• B. ${145}^o$
• C. ${120}^o$
• D. ${95}^o$

Answer 1

The correct option is B ${145}^o$

$\angle CHG$ and $\angle GHD$ are supplementary angles.

$\angle CHG$ $+$ $\angle GHD$$={180}^{\circ }$

$\Rightarrow$ $\angle GHD={120}^{\circ }$

We can observe that $\angle GHK$ and $\angle HKL$ are alternate interior angles.

$\therefore$ $\angle HKL=\angle GHK$

$\Rightarrow$ $\angle HKL$=$\angle GHD$$+$$\angle DHK$

$\Rightarrow$ $\angle HKL$ $=$ ${145}^{\circ }$

Hence, option B is correct.