(i) The diagram below shows two chords, \(PQ\) and \(QR\) which meet at point \(Q\) at the circumference of the circle.
\(\angle PQR \) is the angle at the circumference of the circle subtended by the arc \(PR\).
(ii)
\(\angle PQS\) and \(\angle PRS\) are angles at the circumference of the circle subtended by the major arc \(PS\).
\(\angle QPR\) and \(\angle QSR\) are angles at the circumference of the circle subtended by the minor arc \(QR\).
The following diagram shows a circle with a length of arcs \(PR=QS\).
Determine the value of \(x\).
The value of \(x=40 {^\circ}\).
This is because \(\angle x\) and \(\angle 40{^\circ}\) are at the circumference and the length of arcs \(PR=QS\).
The following diagram shows a circle.
Determine the value of \(x\) and \(y\) .
The value of \(x \) is \(35^\circ\).
Meanwhile, the value of \(y\) is
\(\begin{aligned} y&= 35{^\circ}(2) \\\\y&= 70{^\circ}. \end{aligned}\)
For central angles of a circle subtended by an arc:
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