question_answer

If \[\overrightarrow{OP}\] is a ray standing on a line \[\overleftrightarrow{OR}\] such that \[\angle POQ=\angle POR,\] what is the measure \[\angle POQ\]?

A)  \[{{45}^{o}}\]                   

B)         \[{{60}^{o}}\] 

C)   \[{{75}^{o}}\]                  

D)         \[{{90}^{o}}\]  

Correct Answer: D

Solution :

   Given OP is a ray on line QR. Also \[\angle POQ=\angle POR.\] \[\angle POQ=\angle POR\]                        ?..(i) \[\angle POQ+\angle POR={{180}^{o}}\]                               ?..(ii) From (1) and (2), we have \[2\angle POQ={{180}^{o}}\] \[\Rightarrow \] \[\angle POQ=\frac{{{180}^{o}}}{2}={{90}^{o}}\]