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From the figure, find the measure of the unknown angle \(x\) and state the theorem used in finding the same.
In the given figure, \(O\) is the centre and the arcs \(PS\) and \(QR\) are equal.
1. The measure of \(\angle\)\(POS\) is
2. The theorem used in finding the unknown angle \(x\) is
Answer variants:
If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle
Angles in the same segment of a circle are equal
Equal arcs of a circle subtend equal angles at the centre
Equal chords of a circle subtend equal angles at the centre
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