9th Class
Mathematics
Geometry
Question Bank
Geometry
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 \[\angle QCR={{125}^{o}}\]