Three points P, Q, R, and S are located on the circumference of a circle. If angle RPS = $ 30^\circ and \angle PQS = 40^\circ deg , what is the measure of \PRS?
Three points P, Q, R, and S are located on the circumference of a circle. If $\angle \text{RPS} = 30^\circ \text{and} \angle \text{PQS} = 40^\circ$ , what is the measure of $\angle\text {PRS}$ ?
तीन बिंदु P, Q, R और ऽ एक वृत्त की परिधि पर स्थित हैं। $\angle \text{RPS} = 30^\circ \text{and} \angle \text{PQS} = 40^\circ$ का माप क्या है $\angle\text {PRS}$
Detailed Solution & Logic
Correct Answer:
$ 40^\circ $
Solution:
In a circle, angles standing on the same chord are equal.
Here, $\angle PQS$ and $\angle PRS$ stand on the same chord $PS$.
Therefore,
$\angle PRS = \angle PQS = 40^\circ$
(The given $\angle RPS = 30^\circ$ is not required.)
Answer: ${40^\circ}$
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