question_answer

Lines PQ and RS intersect at O. If \[\angle POS=2\,\,\angle SOQ\] ,then the four angles at O are

A) \[30{}^\circ ,\text{ }30{}^\circ ,\text{ }120{}^\circ ,\text{ }180{}^\circ \]

B) \[60{}^\circ ,\text{ }60{}^\circ ,\text{ }120{}^\circ ,\text{ }120{}^\circ \]  

C) \[60{}^\circ ,\text{ }90{}^\circ ,\text{ }90{}^\circ ,\text{ }120{}^\circ \]

D) \[30{}^\circ ,\text{ }60{}^\circ ,\text{ }90{}^\circ ,\text{ }180{}^\circ \]

Correct Answer: B

Solution :

 \[\angle SOQ=\alpha \] then      \[\angle POS=2\alpha \] \[\therefore \]  \[\alpha +2\alpha ={{180}^{o}}\]                 \[\alpha ={{60}^{o}}\]                 Hence, angles are \[\alpha ,\alpha ,2\alpha \]and \[2\alpha \] i.e. \[{{60}^{o}},\text{ }{{60}^{o}},\text{ }{{120}^{o}}\]and \[{{120}^{o}}\].