Concept:Angles in the same segment are equal, and base angles of an isosceles triangle are equal.Explanation:In the circle, ∠RSQ and ∠RPQ subtend the same chord RQ.Therefore, ∠RSQ=∠RPQ=48∘.Since ∣SR∣=∣QR∣, triangle SRQ is isosceles.Thus, the base angles are equal:∠SQR=∠RSQ=48∘.Using the angle sum of triangle SRQ:∠QRS+48∘+48∘=180∘∠QRS=180∘−96∘=84∘.Given ∠SRP=65∘, which is the same as ∠PRS=65∘.From the diagram:∠PRQ=∠QRS−∠PRS∠PRQ=84∘−65∘=19∘.Answer:∠PRQ=19∘.The correct option is D.
