Question

In the given figure(not drawn to scale), $ABCD$ is a trapezium with $AD$ parallel to $BC$. $JDK,GHCI,EABF$ are straight and parallel lines. Find $x-y$.

• A. ${58}^o$
• B. ${68}^o$
• C. ${71}^o$
• D. ${48}^o$

Answer 1

The correct option is D ${48}^o$

Since $JDK$ and $GHCI$ are parallel lines

$\angle HCD={48}^{\circ }$ ....Alternate interior angle as shown in the figure

$\angle x$ is exterior angle of $\Delta DHC$

$\angle x=\angle y+\angle HCD$ .....By exterior angle property

$\Rightarrow \angle x=\angle y+{48}^{\circ }$

$\Rightarrow \angle x-\angle y={48}^{\circ }$