Question

In the given figure find $\angle ABQ$:

• A. ${45}^o$
• B. ${50}^o$
• C. ${65}^o$
• D. ${75}^o$

Answer 1

The correct option is B ${50}^o$

$\angle AOB={100}^{\circ }$

$\therefore \angle OAB=\angle OBA..$ Same arc

$\therefore \angle OAB=\angle OBA=\frac{180-100}{2}$

$\therefore \angle OBA={40}^{\circ }$

Now $\angle ABQ+\angle OBA={90}^{\circ }$

$\therefore \angle ABQ={90}^o-{40}^o$

$\therefore \angle ABQ={50}^{\circ }$