question_answer

In\[\Delta ABC,\]\[\angle A=90{}^\circ ,\]\[\angle C=55{}^\circ ,\]\[AD\bot BC.\] What is the value of\[\angle BAD\]?             [SSC (CGL) 2013]

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

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

C) \[55{}^\circ \]  

D) \[35{}^\circ \]

Correct Answer: C

Solution :

            

\[\because \]\[AD\bot BC,\]\[\angle ADC=\angle ADB=90{}^\circ \]

\[\therefore \]\[\angle B=180{}^\circ -\,\,(90{}^\circ -55{}^\circ )=35{}^\circ \]

[by sum property of triangle]

Now, in\[\Delta ADC,\] the sum of three angles of a triangle is \[180{}^\circ .\]

\[\therefore \]\[\angle ADC+\angle ACD+\angle DAC=180{}^\circ \]

\[\Rightarrow \]\[\angle DAC=180{}^\circ -90{}^\circ -55{}^\circ =35{}^\circ \]

\[\angle BAD=90{}^\circ -35{}^\circ =55{}^\circ \]