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In the given figure, O is the centre of the circle. AB and AC are tangents drawn to the circle from point A. If $\angle BAC = 65^\circ$, then find the measure of $\angle BOC$.
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$\angle BAC + \angle BOC = 180^\circ$
$\Rightarrow \angle BOC = 180^\circ - 65^\circ$
$\Rightarrow \angle BOC = 115^\circ$
$\Rightarrow \angle BOC = 180^\circ - 65^\circ$
$\Rightarrow \angle BOC = 115^\circ$