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The problem you provided involves finding the measure of \( \angle QPR \), given certain information about other angles.

### Given:
- \( m\angle QPS = 107^\circ \)
- \( m\angle RPS = 4x + 27^\circ \)
- \( m\angle QPR = 9x - 115^\circ \)

### To find: \( m\angle QPR \).

The diagram indicates that \( \angle QPS \), \( \angle RPS \), and \( \angle QPR \) are related geometrically. From the arrangement of the diagram, it appears that angles \( \angle QPS \), \( \angle RPS \), and \( \angle QPR \) might sum to a certain value depending on their positioning (either supplementary or forming a triangle). This would likely require solving for \( x \).

Do you want me to solve for \( x \) first and find the exact measure of \( m\angle QPR \)?

Find the measure of \( \angle QPR \) given that \( m\angle QPS = 107^\circ \), \( m\angle RPS = 4x + 27^\circ \), and \( m\angle QPR = 9x - 115^\circ \).

Learn how to find the measure of an angle using given geometric properties and algebraic expressions. This problem covers core concepts such as angle relationships, linear pairs, and solving equations. Suitable for students in Grades 8-10.

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