A) \[{{x}^{o}}+2{{y}^{o}}={{90}^{o}}\]
B) \[2{{x}^{o}}+{{y}^{o}}={{90}^{o}}\]
C) \[{{x}^{o}}+{{y}^{o}}={{120}^{o}}\]
D) \[3{{x}^{o}}+2{{y}^{o}}={{120}^{o}}\]
Correct Answer: A
Solution :
Consider chord QR \[\therefore \] \[\angle QRP=\angle QSR\] \[\Rightarrow \] \[\angle QSR={{y}^{o}}\] \[[\because \,\,\,\angle QRP={{y}^{o}}]\] \[\Rightarrow \] \[\angle PSR={{y}^{o}}\] Since angle in a semicircle is a right angle. \[\therefore \] \[\angle QRS={{90}^{o}}\] Now, \[\angle PRS=\angle QRP+\angle QRS\Rightarrow \angle PRS={{y}^{o}}+{{90}^{o}}\]In \[\Delta \,PRS,\] we have \[\angle SPR+\angle PRS+\angle PSR={{180}^{o}}\] \[\Rightarrow \] \[{{x}^{o}}+{{y}^{o}}+{{90}^{o}}+{{y}^{o}}={{180}^{o}}\] [Given,\[\angle SPP={{x}^{o}}\]] \[\Rightarrow \] \[{{x}^{o}}+2{{y}^{o}}={{90}^{o}}\]
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