question_answer

'O' is the centre of a circle,\[\angle BOA={{90}^{o}}\] and \[\angle COA={{110}^{o}}.\]Find the measure of \[\angle BAC.\]

A) \[70{}^\circ \]

B) \[80{}^\circ \]

C) \[120{}^\circ \]

D) \[50{}^\circ \]

Correct Answer: B

Solution :

\[\angle OAC=\frac{{{180}^{o}}-{{110}^{o}}}{2}={{35}^{o}}\] \[\angle OAB=\frac{{{180}^{o}}-{{90}^{o}}}{2}={{45}^{o}}\] \[\angle BAC={{35}^{o}}+{{45}^{o}}={{80}^{o}}\]