Given the angles in the problem, we need to solve for the measure of $\angle PQS$.

The angles involved are:

• $m\angle PQR = 104^\circ$
• $m\angle SQR = 56^\circ$

To solve for $m\angle PQS$, we can use the fact that $m\angle PQS = m\angle PQR - m\angle SQR$.

Solution:

$m\angle PQS = m\angle PQR - m\angle SQR$

Substituting the given values:

$m\angle PQS = 104^\circ - 56^\circ$

$m\angle PQS = 48^\circ$

Final Answer:

The measure of $\angle PQS$ is $48^\circ$.

Would you like any further details or have any questions? Here are some related questions:

1. How do you determine if two angles are supplementary?
2. What is the relationship between adjacent angles?
3. Can you solve for an unknown angle in a triangle given two angles?
4. How do you calculate the angle sum of a quadrilateral?
5. What are complementary angles?

Tip: When dealing with angles around a point, remember that the sum of all angles around a point is $360^\circ$.