question_answer

If in triangles PQR and LMN, \[\angle P=\angle M=60{}^\circ \], \[\text{PQ}\,\,\text{:}\,\,\text{ML}\,\,\text{=}\,\,\text{PR}\,\,\text{:}\,\text{ MN}\] and \[\angle N=55{}^\circ \], then \[\angle \text{Q}\] is

A) \[50{}^\circ \]

B) \[55{}^\circ \]

C) \[65{}^\circ \]  

D) \[75{}^\circ \]

Correct Answer: C

Solution :

 It is clear that \[\Delta s\] PQR and LMN are similar                 \[\therefore \]  \[\angle R=\angle N={{55}^{o}}\] Hence      \[\angle Q={{180}^{o}}-(\angle P+\angle R)\]                 \[={{180}^{o}}-({{60}^{o}}+{{55}^{o}})={{65}^{o}}\]