Question

$LP$ is the angle bisector of $\angle MLN$. Find $x.$

• A. ${45}^o$
• B. ${30}^o$
• C. ${65}^o$
• D. none of the above

Answer 1

The correct option is A ${45}^o$

In $△LMN$ using angle sum property of triangle.

$\angle MLN+\angle M+\angle N={180}^{\circ }\angle MLN+{45}^{\circ }+{45}^{\circ }={180}^{\circ }\Rightarrow \angle MLN={180}^{\circ }-{90}^{\circ }={90}^{\circ }$

Now $LP$ is the angle bisector of $\angle MLN$ , so it divides $\angle MLN$ in two equal angles.

$\Rightarrow x^{\circ }=\frac{{90}^{\circ }}{2}={45}^{\circ }$