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Angle Subtended by Diameter on the Circle

In the given ...

Question

In the given figure, PQ is the diameter of the circle whose centre is O.

Given $∠$ ROS = $42^{o}$ , calculate $∠$ RTS

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Solution

Join P and S as shown in the diagram.

$\angle PSQ = 90^o$ (angle in a semi circle)

$\angle SPR = \frac{1}{2} \angle ROS$

(Both angles are subtended by the chord SR)

$\Rightarrow \angle SPT = \frac{1}{2} \times 42^o = 21^o$

In $\triangle PST$

$\angle PST = 90^o-\angle SPT$

$\Rightarrow \angle RTS = 90^o-21^o = 69^o$

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