Question

In the given figure O is the centre of the circle What is the value of $\angle PQB$?

• A. ${50}^{\circ }$
• B. ${60}^{\circ }$
• C. ${65}^{\circ }$
• D. ${70}^{\circ }$

Answer 1

The correct option is B ${60}^{\circ }$

$\Rightarrow$ In $△PAB$

$\Rightarrow$ $\angle PBA={30}^o$ [ Given ]

$\Rightarrow$ $\angle APB={90}^o$ [ Angle inscribed in a semi-circle ]

$\Rightarrow$ $\angle PAB+\angle PBA+\angle APB={180}^o$

$\Rightarrow$ $\angle PAB+{30}^o+{90}^o={180}^o$

$\Rightarrow$ $\angle PAB={180}^o-{120}^0={60}^o$

$\Rightarrow$ $\angle PAB=\angle PQB$ [ Angles inscribed in same arc PB ]

$\therefore$ $\angle PQB={60}^o$