Determine the value of \( x \), where \( O \) is the center of the circle and \( AB \) is the diameter of the circle.

Q.Determine the value of \( x \), where \( O \) is the center of the circle and \( AB \) is the diameter of the circle.

\[ \angle POB = 180^\circ - 120^\circ = 60^\circ \] \[ \because \text{The central angle } \angle POB \text{ subtends arc PB, and the inscribed angle } \angle PQB = x^\circ \] \[ \therefore x^\circ = \cfrac{1}{2} \times \angle POB = \cfrac{1}{2} \times 60^\circ = 30^\circ \] \[ \therefore x = 30 \]