If AB is a chord of a circle and P and Q are two points on the circle different from A and B, then:
The angle subtended by AB at P and Q are either equal or supplementary.
Since AB is a chord and P, Q are two points different from A and B, two cases arise:
Case 1: If P and Q are on the same side of the chord, angles subtended by the chords at P and Q are equal.
Case 2: If P and Q are on the opposite side of the chord, angles subtended by the chord are supplementary.