Question

In the adjoining figure find the measure of $\angle BACif\angle ABD=\angle CADand\angle BAD=\angle ACD$

• A. ${120}^0$
• B. ${60}^0$
• C. ${75}^0$
• D. ${90}^0$

Answer 1

The correct option is D ${90}^0$

Let, $\angle BAD=\angle ACD=x$

and $\angle ABD=\angle CAD=y$

Now, $\angle C+\angle A+\angle B=180°$

$x+(x+y)+y=180°$

$x+y=90°$

also, $\angle A=\angle BAC=\angle BAD+\angle CAD=x+y$

So, $\angle BAC=90°$