In the given figure O is the centre of the circle. IF angle PRQ = 64°, then what is measure of angle OPQ ?
Answer & explanation
Correct answer: option 1
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°