6. In the diagram, $P, Q$ and $R$ are three points on the circle whose centre is $O$. The lines $P O$ and $Q R$ are produced to meet at $S$. Suppose that $R S=O P$, and $\angle P S Q=12^{\circ}$ and $\angle P O Q=x^{\circ}$. Find the value of $x$.
(A) 36
(B) 42
(C) 48
(D) 54
(E) 60
6. Ans: A
Since $R S=O P$, we have $R S=O R$. Hence, $\angle R O S=\angle R S O=12^{\circ}$. Then
$$
\angle O Q R=\angle O R Q=2 \times 12^{\circ}=24^{\circ} .
$$

Thus,
$$
\begin{aligned}
\angle P O Q & =180^{\circ}-\angle Q O R-\angle R O S \\
& =180^{\circ}-\left(180^{\circ}-24^{\circ}-24^{\circ}\right)-12^{\circ} \\
& =36^{\circ} .
\end{aligned}
$$