In the given figure O is the centre of the circle. IF angle PRQ = 64°, then what is  measure of angle OPQ ?

26° 32° 64° 60°

26°

We know that, Chord PQ makes ∠PRQ at the circumference and ∠POQ at center of circle. Let ∠POQ = a, ∠OPQ = b = ∠POQ = 2 × 64°  = a = 128°  In ΔPOQ, OP = OQ = ∠OPQ = ∠OQP = b Now, In ΔPOQ,  ∠ POQ + ∠OPQ + ∠OQP = 180°  = 128° + b + b = 180°  = 2b = 180° – 128°  = b = 52°/2 = b = 26°