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Question

PQRS is a cyclic quadrilateral and PQ is the diameter of the circle. If ∠RPQ = 38°, then what is the value (in degrees) of ∠PSR?

This question was previously asked in
SSC CGL 2017 (Tier 1) Previous Year Paper (16-Aug-2017) (Shift 1)
The correct answer is

128

Step 1 — Angle in semicircle: Since PQ is the diameter, \(\angle PRQ=90^\circ\).

Step 2 — Find \(\angle PQR\) in \(\triangle PQR\):

\[\angle PQR=180^\circ-90^\circ-38^\circ=52^\circ\]

Step 3 — Cyclic quadrilateral property: Opposite angles sum to \(180^\circ\), so \(\angle PSR+\angle PQR=180^\circ\).

\[\angle PSR=180^\circ-52^\circ=128^\circ\]

Therefore \(\angle PSR=128^\circ\).

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Important Questions from Quadrilaterals

  1. ABCD is a quadrilateral such that $\angle A = 47^\circ$, $\angle B = 66^\circ$, $\angle C = 133^\circ$ and $\angle D = 114^\circ$. What type of a quadrilateral is ABCD?

  2. What is the main purpose of cell division in multicellular organisms?
  3. Which of the following organelles is the first to divide during binary fission in Amoeba?
  4. The sum of all internal angles of a quadrilateral is:
  5. If ABCD is a cyclic quadrilateral and ABC is an equilateral triangle find the angle of CDA.
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