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To solve this problem, we can use the property of cyclic quadrilaterals in a circle, which states that opposite angles of a cyclic quadrilateral sum to \(180^\circ\).

### Given:
- \(\angle QRS = 29^\circ\)
- \(\angle SQP = 25^\circ\)
- \(\angle SQR = x^\circ\) (the unknown value we need to find)

We observe that triangle \(SQR\) is inscribed in the circle, and \(\angle P\) and \(\angle QRS\) are opposite angles in the cyclic quadrilateral \(SQRP\).

Using the rule for opposite angles in cyclic quadrilaterals:
\[
\angle QRS + \angle SQP = 180^\circ
\]
Substituting the given values:
\[
29^\circ + x = 180^\circ
\]
Solve for \(x\):
\[
x = 180^\circ - 29^\circ = 151^\circ
\]

Thus, the value of \(x\) is \(151^\circ\).

Would you like more details, or do you have any questions about this? Here are some related questions to consider:

1. What are cyclic quadrilaterals, and how are their properties used in solving geometry problems?
2. Can the sum of angles inside a cyclic quadrilateral ever be more or less than 360°?
3. How does the inscribed angle theorem help in solving circle problems?
4. Are all quadrilaterals inside a circle considered cyclic? Why or why not?
5. What is the relationship between angles in a triangle inscribed in a circle and the circle's arc?

**Tip:** Always look for cyclic quadrilaterals in circle geometry questions, as they provide useful angle relationships.

Find the value of x in a cyclic quadrilateral inscribed in a circle, given that angle QRS = 29 degrees, angle SQP = 25 degrees.

Solve for x in a cyclic quadrilateral inscribed in a circle where angle QRS is 29 degrees, and angle SQP is 25 degrees. Learn about cyclic quadrilaterals and how to use their properties to find unknown angles.

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