OABC is a quadrilateral, where O is the centre of a circle and A, B,C are points in the circle, such that $$\angle$$ABC = $$120^\circ$$. What is the ratio of the measure of $$\angle$$AOC to that of $$\angle$$OAC ?

OABC is a quadrilateral, ABCD is a cyclic quadrilateral and AC is a chord

Given $$\angle ABC=120^\circ$$ 

So, $$\angle ADC=60^\circ$$  (In cyclic quadrilateral sum of opposite sides angle are $$180^\circ$$)

$$\angle AOC=2(\angle ADC) = 120^\circ$$  (The angle from the same arc at the centre is twice the angle at the cirmference)

In \triangle AOC, OC=OA= radius and $$\angle AOC= 120^\circ$$ 

So,  $$\angle OAC= \angle OCA=30^\circ$$

Hence,$$\angle AOC:\angle OAC$$=4:1