A) \[{{175}^{{}^\circ }}\]
B) \[{{208}^{{}^\circ }}\]
C) \[{{214}^{{}^\circ }}\]
D) \[{{250}^{{}^\circ }}\]
Correct Answer: D
Solution :
(d):- \[x=\angle VTR={{56}^{{}^\circ }}\] (Since, PTMR is a cyclic quadrilateral, \[x+z={{180}^{{}^\circ }}\] \[\Rightarrow {{56}^{{}^\circ }}+z={{180}^{{}^\circ }}\] \[\Rightarrow \]\[z={{124}^{{}^\circ }}\] In \[\Delta PTR,\] \[PT=TR\] \[x=\angle 1={{56}^{{}^\circ }}\] \[\angle PTU=\angle 1={{56}^{{}^\circ }}\Rightarrow \angle QTU=y+{{56}^{{}^\circ }}\] \[\Rightarrow \]\[{{90}^{{}^\circ }}=y+{{56}^{{}^\circ }}\Rightarrow y={{34}^{{}^\circ }}\] \[\therefore \]\[x+y+z={{56}^{{}^\circ }}+{{34}^{{}^\circ }}+{{124}^{{}^\circ }}={{214}^{{}^\circ }}\]You need to login to perform this action.
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