In the diagram, O is the centre of the circle. If SOQ is a diameter and < PRS is 38∘ ∘ , what is the value of < PSQ

In the diagram, O is the centre of the circle. If SOQ is a diameter and < PRS is 38${}^{\circ }$, what is the value of < PSQ

Answer Details

Since SOQ is a diameter of the circle, angle SPQ = 90 degrees (angles subtended by a diameter are always 90 degrees). Therefore, angle PSQ is the difference between angle PRS and angle SPQ. Angle PSQ = angle PRS - angle SPQ = 38 - 90 = -52 degrees. However, since angles in a circle add up to 360 degrees, we can add 360 degrees to -52 to get the equivalent angle in the circle. Angle PSQ = -52 + 360 = 308 degrees. Therefore, the value of angle PSQ is 308 degrees. So the correct option is: 52∘.