The question is asking for the relationship between $\angle PSQ$ and $\angle RSQ$, where the angles are inside a circle with $\angle PSQ = x$ and $\angle RSQ = 2x$.

Analyzing the Diagram:

Given the points $P$, $Q$, $R$, and $S$ on the circle:

1. $\angle PSQ$ is the angle at the center subtended by arc $PQ$.
2. $\angle RSQ$ is the angle at the center subtended by arc $RQ$.

According to the properties of circles, the angle subtended by an arc at the center of the circle is twice the angle subtended by the same arc at any point on the circumference. Therefore:

$\angle PSQ = \frac{1}{2} \times \angle RSQ$

Given that $\angle RSQ = 2x$, it follows that:

$\angle PSQ = \frac{1}{2} \times 2x = x$

So the relationship is indeed:

$\angle PSQ$ is half of $\angle RSQ$.

Answer:

The correct answer is Option A: $\angle PSQ$ adalah separuh daripada $\angle RSQ$ (which means "$\angle PSQ$ is half of $\angle RSQ$").

Would you like more details, or do you have any questions? Here are some related questions to consider:

1. How do you calculate the angle subtended by an arc at the center of a circle?
2. What is the relationship between angles subtended at the center and at the circumference by the same arc?
3. How can you find the measure of an angle formed by two chords intersecting inside a circle?
4. How does the Inscribed Angle Theorem relate to this problem?
5. What are the properties of angles formed by tangents and chords?

Tip: Remember that in any circle, the angle subtended by an arc at the center is always twice the angle subtended by the same arc at any other point on the circumference.