In the given figure, PQ is the diameter of the circle whose centre is O. Given ∠ROS = 42°, Calculate ∠RTS.
Exercise 17 (A) | Q 50 | Page 262
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∠PSQ = 90°
(Angle in a semicircle)
Also, $\angle S P R=\frac{1}{2} \angle R O S$
(Angle ate the centre is double the angle at the circumference subtended by the same chord)
$\Rightarrow S P T=\frac{1}{2} \times 42^{\circ}=21^{\circ}$
∴ In right triangle PST,
∠PTS = 90° -∠SPT
⇒ ∠RTS = 90°- 21° = 69°
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