Question

In the adjoining figure ${}^{\prime }{O}^{\prime }$ is the center of circle, $\angle$CAO $=$ ${25}^{\circ }$ and $\angle$CBO $=$ ${35}^{\circ }$. What is the value of $\angle$AOB?

• A. 55°
• B. 110°
• C. 120°
• D. Data insufficient

Answer 1

The correct option is C

120°

Let $\angle$ACB $=x\Rightarrow \angle$AOB $=2x$ [Angle subtended at centre of a circle]

In triangle, OAB

As OA $=$ OB [radius]

$\angle$OAB $=$ $\angle$OBA $={90}^{\circ }–x$ [$\angle$OAB $+\angle$OBA $+\angle$AOB $={180}^{\circ }$]

Consider triangle, ABC

$\angle$A $+\angle$B $+\angle$C $={180}^{\circ }$

$\Rightarrow x+{25}^{\circ }+{90}^{\circ }–x+{90}^{\circ }–x+{35}^{\circ }={180}^{\circ }$

$\Rightarrow x={60}^{\circ }$

$\Rightarrow \angle$AOB $=2x=2\times {60}^{\circ }={120}^{\circ }$.