Question

In given figure $AB||CD||EF$ and $GH||KL,$ The measure of $\angle HKL,$ is

• A. ${85}^{\circ }$
• B. ${135}^{\circ }$
• C. ${145}^{\circ }$
• D. ${215}^{\circ }$

Answer 1

The correct option is C ${145}^{\circ }$

Let us extend the line $GH$ to $N$ such that it intersects the line $AB$ at $M$

$AB||CD$ and $GM$ is transversal

$⟹$ The $\angle AMH=\angle CHG={60}^{\circ }$ $\left(\text{Corresponding Angles}\right)$

$\angle NMB=\angle AMH={60}^{\circ }$ $\left(\text{Vertically opposite angles}\right)$

$AB||CD$ and $HK$ is transversal

$⟹$ The $\angle AKH=\angle KHD={25}^{\circ }$ $\left(\text{Alternate interior Angles}\right)$

$NM||KL$ and $KM$ is transversal

$⟹$ The $\angle NMK=\angle LKB={60}^{\circ }$ $\left(\text{Corresponding Angles}\right)$

$⟹\angle LKM={180}^{\circ }-\angle KLB\left(\text{Linear pair}\right)$

$⟹\angle LKM=180-60={120}^{\circ }$

$⟹\angle HKL=\angle HKA+\angle AKL$

$⟹\angle HKL=25+120={145}^{\circ }$