Find the required angle — task. Mathematics State Board, Class 9.

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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

$45^{\circ}$
$360^{\circ}$
$90^{\circ}$
$180^{\circ}$

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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4. Find the required angle

Exercise condition: