TP is a line that tangent to a circle centered at O. If PQ∥TO and ∠OTP=28∘, find the measure of ∠POQ in degrees.
Let the tangent to the circle be TPR then,
∠OTP = ∠QPR = 28° ...[PQ∥TO and corres. angles]
OP ⊥ TR ...[TR is a tangent and OP is the radius]
⇒ ∠OPR = 90°
∠OPQ = ∠OPR - ∠QPR = 90 - 28 = 62
∠OPQ = 62°
∵ OP = OQ ...[radii of circle]
⇒ ∠OPQ = ∠OQP = 62°
In △OPQ
∠OPQ + ∠OQP + ∠POQ = 180
∠POQ = 180 - 124
∠POQ = 56°