In the given figure, PQ is a diameter. Chord SR is parallel to PQ. Given that ∠PQR = 58°,
Calculate:
(i) ∠RPQ, (ii) ∠STP
Calculate:
(i) ∠RPQ, (ii) ∠STP
Exercise 17 (A) | Q 51 | Page 262
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(i) ∠PRQ = 90°
(Angle in a semicircle)
∴ In right triangle PQR,
∠RPQ = 90° - ∠PQR = 90° - 58° = 32°
(ii) Also, SR || PQ
∠PRS = ∠RPQ = 32 (Alternate angles) In cyclic quadrilateral PRST,
∠STP =180° - ∠PRS = 180° - 32° = 148°
(pair of opposite angles in a cyclic quadrilateral are supplementary)
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