PQ is a chord in the minor segment of a circle and R is a point on the minor arc PQ. The tangents at the points P and Q meet at the point T. If ∠PRQ =102°, then the measure of ∠PTQ is :

Correct option is A

​$$\textbf{Given :} \\\ \, \\\angle PRQ = 102^\circ \\\ \, \\R \text{ lies on the minor arc } PQ \\\ \, \\\textbf{Formula Used :} \\\ \, \\\text{Angle at center} = 2 \times \text{Angle at circumference} \\\ \, \\\angle PTQ = 180^\circ - \angle POQ \\\ \, \\\textbf{Solution :} \\\ \, \\\text{Major arc } PQ = 2 \times 102^\circ = 204^\circ \\\ \, \\\text{Minor arc } PQ = 360^\circ - 204^\circ = 156^\circ \\\ \, \\\angle POQ = 156^\circ \\\ \, \\\angle PTQ = 180^\circ - 156^\circ = 24^\circ \\\ \, \\\textbf{Final Answer :} \\\ \, \\24^\circ$$​​