Question

The figure below is not drawn to scale. If all lines are straight lines, then which of the following options is FALSE?

• A. AB || GH
• B. CD || IJ
• C. DR || SK
• D. EF || KL

Answer 1

The correct option is D EF || KL

$A)$ $\angle ABT=\angle GHB={120}^{\circ }$ (corresponding angles)

$\Rightarrow AB\parallel GH$

$\Rightarrow \left[A\right]$ is correct.

$B)$ $\angle CDJ+\angle IJD={180}^{\circ }$ (supplementary angles)

$\Rightarrow CD\parallel IJ$

$\Rightarrow \left[B\right]$ is correct.

$C)$ $\angle DEK={180}^{\circ }-\angle FEK={180}^{\circ }-{70}^{\circ }={110}^{\circ }$

But $\angle DEK=\angle CDJ={110}^{\circ }$ (corresponding angles)

$\Rightarrow DR\parallel SK$

$\Rightarrow \left[C\right]$ is correct.

$D)$ $inner\angle EKL={360}^{\circ }-outer\angle EKL={360}^{\circ }-{260}^{\circ }={100}^{\circ }$

$\angle EKL+\angle FEK={100}^{\circ }+{70}^{\circ }={170}^{\circ }\ne {180}^{\circ }$

$\Rightarrow EFnot\parallel KL$

$\Rightarrow \left[D\right]$ is false.