A) \[{{30}^{{}^\circ }}\]
B) \[{{35}^{{}^\circ }}\]
C) \[{{100}^{{}^\circ }}\]
D) \[{{60}^{{}^\circ }}\]
Correct Answer: B
Solution :
(b): \[\angle PQS={{60}^{{}^\circ }}\] \[\angle QCR={{130}^{{}^\circ }}\] \[\therefore \]\[\angle QPR=\frac{1}{2}\times {{130}^{{}^\circ }}={{65}^{{}^\circ }}\] \[\Rightarrow \]\[\angle QRP={{180}^{{}^\circ }}-{{60}^{{}^\circ }}-{{65}^{{}^\circ }}={{55}^{{}^\circ }}\] \[\Rightarrow \]\[\angle PCQ={{110}^{{}^\circ }}\] \[\therefore \]In \[\Delta QCR,\] \[QC=CR\] \[\Rightarrow \]\[\angle CQR=\angle CRQ={{25}^{{}^\circ }}\] \[\left[ \therefore \angle CQR+\angle CRQ={{50}^{{}^\circ }} \right]\] \[\therefore \]\[\angle PQC+\angle QPC={{35}^{{}^\circ }}\] \[\left[ \therefore \angle PQC+\angle QPC={{70}^{{}^\circ }} \right]\] Similarly, \[\angle CPR={{30}^{{}^\circ }}\] \[\therefore \]\[\angle RPS={{35}^{{}^\circ }}\]You need to login to perform this action.
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