Question 7. (a) In the figure given below, PQ is a diameter. Chord SR is parallel to PQ.Given ∠PQR = 58°, calculate (i) ∠RPQ (ii) ∠STP (T is a point on the minor arc SP)

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deepaksoniGuru

Asked: March 31, 20212021-03-31T13:26:17+05:30 2021-03-31T13:26:17+05:30In: ICSE

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)

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AAREKH · Answer 1 · 2021-04-01T06:20:06+05:30

AAREKH Guru

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