question_answer

ABCD is a parallelogram in which \[-D\,\,DAB={{75}^{\text{o}}}\] and \[-D\,DBC={{60}^{\text{o}}}\] then \[-DCDB=\]???.

A) \[60{}^\circ \]                       

B)           \[75{}^\circ \]

C) \[45{}^\circ \]     

D)           \[135{}^\circ \]

Correct Answer: C

Solution :

      We have \[\angle ADB=\angle CBD={{60}^{\text{o}}}\,\,(\because \,AD||BC)\] In \[\Delta \,ADB\] \[\angle A+\angle ADB+\angle ABD={{180}^{\text{o}}}\] \[{{75}^{\text{o}}}+{{60}^{\text{o}}}+\angle ABD={{180}^{\text{o}}}\] \[\angle ABD={{180}^{\text{o}}}-{{135}^{\text{o}}}\] \[\therefore \]    \[\angle ABD={{45}^{\text{o}}}\]