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The question asks for the sum of the interior angles of a quadrilateral in terms of \( x \). Based on the diagram, the angles of the quadrilateral are labeled as:

- \( 3x \) at \( P \)
- \( 2x + 30^\circ \) at \( Q \)
- \( 2x + 30^\circ \) at \( R \)
- A right angle \( 90^\circ \) at \( S \)

### Steps:
1. The sum of interior angles of any quadrilateral is always \( 360^\circ \).
2. The angles are:
   \[
   3x + (2x + 30^\circ) + (2x + 30^\circ) + 90^\circ = 360^\circ
   \]
3. Simplify the equation:
   \[
   3x + 2x + 30^\circ + 2x + 30^\circ + 90^\circ = 360^\circ
   \]
   \[
   7x + 150^\circ = 360^\circ
   \]
4. Solve for \( x \):
   \[
   7x = 360^\circ - 150^\circ
   \]
   \[
   7x = 210^\circ
   \]
   \[
   x = 30^\circ
   \]

### Conclusion:
The value of \( x \) is \( 30^\circ \). 

Do you have any questions or would you like more details?

Here are some related questions:
1. What is the general formula for the sum of the interior angles of any polygon?
2. How would you find the value of \( x \) in different types of polygons?
3. Can the sum of interior angles ever change in a quadrilateral?
4. What is the difference between interior and exterior angles in a polygon?
5. How can angle properties help in solving geometric problems?

**Tip:** In quadrilaterals, remember that the sum of the interior angles is always 360°, regardless of the type of quadrilateral.

Give the sum of the interior angles in terms of x.

Learn how to find the sum of the interior angles of a quadrilateral in terms of x with a detailed step-by-step solution. This problem covers key geometric concepts and the interior angle sum theorem. Suitable for students in Grades 7-9.

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