question_answer

The internal bisectors of\[\text{I}\] and \[\text{II}\] of \[\text{III}\]meet at C. If \[\text{IV}\] = \[70{}^\circ \], then \[\text{I}\] is

A) \[110{}^\circ \]                 

B) \[125{}^\circ \]

C) \[130{}^\circ \]

D) \[140{}^\circ \]  

Correct Answer: D

Solution :

  Let \[\angle PQR=2x\]and \[\angle PRQ=2y\] From \[\Delta PQR\]                 \[2x+{{70}^{o}}+2y={{180}^{o}}\] or            \[2(x+y)={{110}^{o}}\] or            \[x+y={{55}^{o}}\]                           ?.(i) Also, from \[\Delta \,QCR\]                 \[x+\angle QCR+y={{180}^{o}}\] or            \[(x+y)+\angle QCR={{180}^{o}}\] From equation (i), we get                                 \[{{55}^{o}}+\angle QCR={{180}^{o}}\]                 or            \[\angle QCR={{125}^{o}}\]