Question

A parallelogram is constructed and named KLMN. LP is perpendicular to KL and ML is the angular bisector of $\angle KLP$. Find the value of $\angle KNM$.

• A. ${15}^{\circ }$
• B. ${30}^{\circ }$
• C. ${60}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is D ${45}^{\circ }$

$\angle KLP={90}^{\circ }$
LM is an angular bisector of $\angle KLP$.
$\therefore \angle KLM=\frac{1}{2}\times {90}^{\circ }={45}^{\circ }$
$\angle KLM=\angle KNM$ [opposite angles of a parallelogram are equal]
$\therefore \angle KNM={45}^{\circ }$