Question

In $△LMN,△L={60}^{\circ },\angle M={50}^{\circ }$ If $\angle LMN\sim △PQR$ then the value of $\angle R$ is

• A. ${40}^{\circ }$
• B. ${60}^{\circ }$
• C. ${70}^{\circ }$
• D. ${110}^{\circ }$

Answer 1

The correct option is C ${70}^{\circ }$

$\because △LMN=△PQR$ then

$\angle L=\angle P$,$\angle M=Q$,$\angle N=\angle R$

In $△LMN$$\angle L={60}^{\circ },\angle M={50}^{\circ }$

$\angle L+\angle M+\angle N={180}^{\circ }$

${60}^{\circ }+{50}^{\circ }+\angle N={180}^{\circ }$

$\angle N={180}^{\circ }-{110}^{\circ }$

$\angle N={70}^{\circ }$

$\therefore \angle R={70}^{\circ }$