In a circle, points $P, Q, R$, and $S$ lie on the circumference such that chords $PR$ and $QS$ intersect at the center, and both $\angle RPQ$ and $\angle RSQ$ are subtended by the same arc $RQ$. If $\angle RPQ = 50^\circ$, what is the measure of $\angle RSQ$?

Question

Accepted Answer

50^\circ. Inscribed angles subtending the same arc are equal. Since both $\angle RPQ$ and $\angle RSQ$ stand on arc $RQ$, they are equal, so $\angle RSQ=50^\circ$.

In a circle, points \(P, Q, R\), and \(S\) lie on the circumference such that chords \(PR\) and \(QS\) intersect at the center, and both \(\angle RPQ\) and \(\angle RSQ\) are subtended by the same arc \(RQ\). If \(\angle RPQ = 50^\circ\), what is the measure of \(\angle RSQ\)?

Solution

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