Find the value of x in the adjoining figure, if it is given that PR and QS are diameters of the circle.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 38°
Angles in the same segment of a circle are equal: two angles that stand on the same arc, with their vertices on the rest of the circle, are always equal.
QS is a diameter:
So O lies on SQ and the angle x at S is \(\angle PSQ\)
It stands on arc PQ
PR is a diameter:
So O lies on RP and the given \(38^\circ\) at R is \(\angle PRQ\)
It stands on the same arc PQ
So \(x=\angle PRQ=38^\circ\)
