Geometry

Circles

Medium

Find the value of x in the adjoining figure, if it is given that PR and QS are diameters of the circle.

42°

52°

38°

48°

✅ Correct Option: 3

PR and QS are diameters of the circle, so they both pass through the center O of the circle.

When two diameters intersect at the center, they form vertically opposite angles that are equal, and adjacent angles that are supplementary.

An angle at the circumference is half the angle at the center when both are subtended by the same arc.

The central angle is $76°$ .

$x = \dfrac{76°}{2}$

$x = 38°$

Therefore, the value of $x = 38°$ .

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Solution

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