question_answer

In the given figure, A and B are the centres of two circles that intersect at X and V. PXQ is a straight line. If reflex angle \[QBY={{210}^{o}},\]find obtuse angle PAY.    

A) \[{{210}^{o}}\]                   

B)        \[{{150}^{o}}\]

C)        \[{{160}^{o}}\]                               

D)        \[{{120}^{o}}\]                               

Correct Answer: B

Solution :

                                In quadrilateral YBQX              \[\angle YXQ=\frac{1}{2}\]reflex    \[\angle QBY=\frac{1}{2}\times {{210}^{o}}={{105}^{o}}\]             PQ is a straight line                        \[\Rightarrow \]  \[\angle PXY+\angle YXQ={{180}^{o}}\]       (linear pair) \[\Rightarrow \]   \[\angle PXY={{180}^{o}}-{{105}^{o}}={{75}^{o}}\] Now, in quadrilateral PAYX       \[\angle PXY=\frac{1}{2}\angle PAY\] \[\therefore \]   \[\angle PAY=2\angle PXY={{150}^{o}}\]