find the value of x if line QS bisects angle PQR and angle PQ

If line \( QS \) bisects angle \( \angle PQR \), this means that it divides \( \angle PQR \) into two equal parts.

Let's define the information given in the problem:

- Let \( \angle PQS = \angle SQR \) since line \( QS \) bisects \( \angle PQR \).
  
If you have specific expressions for the angles \( \angle PQS \) and \( \angle SQR \) (e.g., in terms of \( x \)), or if there is any additional information like the measure of \( \angle PQR \), please provide that, and I can help solve for \( x \).

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Understand and solve for x using the Angle Bisector Theorem where line QS bisects angle PQR. Learn how to apply this theorem to find the value of x in a geometric context. Suitable for high school students studying geometry.

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