In the given figure, we are tasked with finding the size of angle $\text{PQS}$. Here's the key information we can extract from the image:

• The angle $\angle SQT = 65^\circ$.
• Line $PR$ is straight, making it a transversal intersecting triangle $SQT$ at point $Q$.

To solve for $\angle PQS$, we can use the fact that:

• $PR$ is a straight line, meaning the angles on a straight line must add up to $180^\circ$.
• Therefore, $\angle PQS + \angle SQT = 180^\circ$.

Thus:

$\angle PQS = 180^\circ - 65^\circ = 115^\circ$

However, because of the exterior angle theorem for triangles, the exterior angle $\angle PQS$ is equal to the sum of the interior opposite angles (which is not relevant in this case since there's no additional information about other angles of triangle $SQT$).

So, the correct angle should be calculated based on further steps.

Would you like more details or have any questions on how this solution was derived?

Here are 5 related questions for practice:

1. How would you find the angle $\angle S$ in a right-angled triangle given two sides?
2. What is the sum of the interior angles of a triangle?
3. How do you find the third angle in a triangle if you know two angles?
4. What is the exterior angle theorem in triangles?
5. What would change if the line $PR$ was not straight?

Tip: When dealing with transversals and straight lines, always remember that angles on a straight line sum to $180^\circ$.