question_answer

In the quadrilateral ABCD shown below, \[\angle DAB=\angle DCX\text{ }=120{}^\circ .\]If\[\angle ABC\text{ }=\text{ }105{}^\circ \], what is \[\angle ADC\] equal to -

A) 45°                   

B) 60°

C) 75°                   

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

Correct Answer: C

Solution :

Given, \[\angle ABC={{105}^{{}^\circ }}\] \[\angle \]DAB = 120° \[\Rightarrow \] \[\angle \]DCX = 120° \[\Rightarrow \] \[\angle \]DCB = 180° - 120° = 60° Angles of a quadrilateral is equal to 360°. \[\therefore \] \[\angle \]ADC = 360° - [120° + 105° + 60°] \[= 360{}^\circ  - 285{}^\circ  =[75{}^\circ ]\]