This is the basic and conceptual question from Chapter name- circles

Topic – Angle properties of circles

Chapter number- 15

In the figure given , PQ is a diameter. Chord SR is parallel to PQ.

It is also Given that ∠PQR = 58°,

Now we have to calculate (i) ∠RPQ (ii) ∠STP (T is a point on the minor arc SP)

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Understanding ICSE Mathematics

Question 7(a)

In ∆PQR,

∠PRQ = 90° (Angle in a semi-circle) and ∠PQR = 58°

∠RPQ = 90° – ∠PQR = 90° – 58° = 32°

SR || PQ (given)

∠SRP = ∠RPQ = 32

^{o }(Alternate angles)Now PRST is a cyclic quadrilateral,

∠STP + ∠SRP = 180

^{o}∠STP = 180

^{o }– 32^{o}= 148^{o}