https://file.aiquickdraw.com/mathbot/file/1726192645873nbi3i5rr.jpg

The problem provided in the image contains the following information:

### Given:
- \( \angle PQR \) is supplementary to \( \angle QRS \)
- \( \angle QRS \) is supplementary to \( \angle TWX \)
- \( \angle PQR = (5x - 48)^\circ \)
- \( \angle TWX = (2x + 30)^\circ \)

### To find:
- The measure of \( \angle QRS \)

### Steps to solve:

1. Since \( \angle PQR \) and \( \angle QRS \) are supplementary, we know:
   \[
   \angle PQR + \angle QRS = 180^\circ
   \]

2. Similarly, since \( \angle QRS \) and \( \angle TWX \) are supplementary:
   \[
   \angle QRS + \angle TWX = 180^\circ
   \]

3. Substituting the expressions for \( \angle PQR \) and \( \angle TWX \) from the given information:
   \[
   (5x - 48) + \angle QRS = 180 \quad \text{(1)}
   \]
   \[
   \angle QRS + (2x + 30) = 180 \quad \text{(2)}
   \]

4. Now, solve these two equations simultaneously. From equation (2), we can solve for \( \angle QRS \):
   \[
   \angle QRS = 180 - (2x + 30) = 150 - 2x \quad \text{(3)}
   \]

5. Substitute equation (3) into equation (1):
   \[
   (5x - 48) + (150 - 2x) = 180
   \]

6. Simplify and solve for \( x \):
   \[
   5x - 48 + 150 - 2x = 180
   \]
   \[
   3x + 102 = 180
   \]
   \[
   3x = 78
   \]
   \[
   x = 26
   \]

7. Now substitute \( x = 26 \) back into equation (3) to find \( \angle QRS \):
   \[
   \angle QRS = 150 - 2(26) = 150 - 52 = 98^\circ
   \]

### Answer:
The measure of \( \angle QRS = 98^\circ \).

Would you like more details or have any other questions?

### Related Questions:
1. What is the measure of \( \angle PQR \) when \( x = 26 \)?
2. How do you verify that the angles are supplementary correctly?
3. What is the measure of \( \angle TWX \) when \( x = 26 \)?
4. How would the result change if the equations were altered?
5. Can you explain why supplementary angles sum to 180°?

### Tip:
Always double-check your solution by substituting the variable's value back into the original equations to ensure accuracy.

Given: ∠PQR is supplementary to ∠QRS, ∠QRS is supplementary to ∠TWX. ∠PQR = (5x - 48)°, ∠TWX = (2x + 30)°. Find the measure of ∠QRS.

Learn how to find the measure of ∠QRS when given two supplementary angle relationships. This algebraic problem involves solving for x using the equations ∠PQR = (5x - 48)° and ∠TWX = (2x + 30)°. Suitable for students in Grades 8-10.

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