Solve for m, angle, P, Q, Sm∠PQS if m, angle, P, Q, R, equals, 104, degreesm∠PQR=104
∘
and m, angle, S, Q, R, equals, 56, degreesm∠SQR=56
∘
.

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 \(360^\circ\).

Learn how to solve for angle PQS using angle PQR and angle SQR measurements. This geometry problem involves calculating angles and understanding their relationships. Suitable for high school students.

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