9th Class
Mathematics
Geometry
Question Bank
Geometry
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 \[\angle Q={{180}^{o}}-(\angle P+\angle R)\] \[={{180}^{o}}-({{60}^{o}}+{{55}^{o}})={{65}^{o}}\]