For the figure given below, find the angle OAB (.in degrees)

Given : $$\angle$$ ACB = $$15^\circ$$

To find : $$\angle$$ OAB = $$x=?$$

Solution : Angle subtended by an arc at the centre is double the angle subtended by the same arc at any other point on the circle.

=> $$\angle$$ AOB = $$2\times15^\circ=30^\circ$$ -------------(i)

Also, in $$\triangle$$ AOB, OA = OB = radius of circle,

=> $$\angle$$ OAB = $$\angle$$ OBA = $$x$$     [Angles opposite to equal sides]

Thus, in $$\triangle$$ AOB

=> $$\angle x+$$ $$\angle x+$$ $$\angle$$ AOB = $$180^\circ$$

=> $$2\angle x=180^\circ-30^\circ$$    [Using equation (i)]

=> $$\angle x=\frac{150^\circ}{2}=75^\circ$$ 

=> Ans - (C)