Question

Find the value of x from the given figure in which O is the center of the circle

• A. $x={50}^{\circ }$
• B. $x={60}^{\circ }$
• C. $x={80}^{\circ }$
• D. $x={90}^{\circ }$

Answer 1

The correct option is A $x={50}^{\circ }$

$\angle BAC$ in a circle with centre O is ${40}^{\circ }$ we have $\angle BOC=2\angle BAC$$=2\times {40}^{\circ }={80}^{\circ }$
In $△BOC,CO=OC$ (Radii of the same circle)
$\Rightarrow \angle B=\angle C=x$
$\therefore x+\angle BOC+x={180}^{\circ }$
$\Rightarrow 2x={180}^{\circ }-\angle BOC$
$\Rightarrow 2x={180}^{\circ }-{80}^{\circ }$
$\Rightarrow 2x={100}^{\circ }$
$\Rightarrow x={50}^{\circ }$