Question

Given that line $AB$ and $CD$ are parallel, then $\angle DNE$ is:

• A. ${100}^{\circ }$
• B. ${105}^{\circ }$
• C. ${110}^{\circ }$
• D. None of the above

Answer 1

The correct option is B ${105}^{\circ }$

Clearly, $\angle FMB=\angle MND={75}^{\circ }$ (Corresponding angles)
$\Rightarrow \angle MND+\angle DNE={180}^{\circ }$ (Linear pair)
$\Rightarrow {75}^{\circ }+\angle DNE={180}^{\circ }$
$\Rightarrow \angle DNE={180}^{\circ }-{75}^{\circ }={105}^{\circ }$