question_answer

In the quadrilateral  ABCD shown below,    \[\angle DAB=\angle DCX=120{}^\circ .\]If \[\angle ABC=105{}^\circ ,\]then     what is the value of \[\angle ADC?\]

A) \[45{}^\circ \]                          

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

C) \[75{}^\circ \]  

D) \[95{}^\circ \]

Correct Answer: C

Solution :

Given,   \[\angle ABC=105{}^\circ \]

\[\angle DAB=120{}^\circ \]\[\Rightarrow \]\[\angle DCX=120{}^\circ \]

\[\Rightarrow \]   \[\angle DCB=180{}^\circ -120{}^\circ =60{}^\circ \]

Since, angles of a quadrilateral is equal to \[360{}^\circ .\]

\[\therefore \]\[\angle ADC=360{}^\circ -[120{}^\circ +105{}^\circ +60{}^\circ ]\]

\[=360{}^\circ -285{}^\circ =75{}^\circ \]