Question : In the given figure, PQ is a chord passing through the centre 'O' of the circle. Calculate $\angle$PQS.
Option 1: 40°
Option 2: 60°
Option 3: 20°
Option 4: 80°
Correct Answer: 20°
Solution :
Here, $\angle SRQ =110°$
The sum of either pair of opposite angles in a cyclic quadrilateral is supplementary, i.e., $180^\circ$.
$\angle SRQ + \angle SPQ = 180°$
So, $\angle SPQ = 180° - \angle SRQ = 180° - 110° = 70°$
$\angle PSQ$ is a right angle $= 90°$ (The angle subtended by a diameter on the circumference of a circle is 90°)
So, $\angle PQS = 180° - (\angle SPQ + \angle PSQ)$
$⇒\angle PQS= 180° - (70° + 90°) = 180° - 160° = 20°$
Hence, the correct answer is 20°.
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