https://file.aiquickdraw.com/mathbot/file/17259791156933jgehhxf.jpg

The image provides a geometric problem involving a circle with several points labeled, angles provided, and a request to find certain arc measures.

Key information provided in the problem:
- In circle \( P \), \( \angle QPS = 15^\circ \) and \( RQ \) is the diameter.
- \( \angle RPT = 105^\circ \).
- The problem asks to find the arc measures for \( \overset{\frown}{QT} \), \( \overset{\frown}{RT} \), and \( \overset{\frown}{QTR} \).

### Key observations:
1. Since \( RQ \) is the diameter, \( \angle PRQ = 90^\circ \) (since the angle subtended by a diameter in a semicircle is always \( 90^\circ \)).
2. \( \angle QPS = 15^\circ \), which is subtended by the arc \( \overset{\frown}{QS} \).
3. The angle at the center is always twice the angle at the circumference subtended by the same arc.

Let's proceed with these principles and the given details.

Would you like me to solve this step by step, or provide further clarification?

In circle P, the measure of ∠QPS is 15° and RQ is a diameter. Find the arc measures m∠QT, m∠RT, and m∠QTR.

Solve a circle geometry problem where ∠QPS = 15° and RQ is the diameter. Learn how to find the arc measures m∠QT, m∠RT, and m∠QTR using key circle properties and theorems. This is ideal for students in Grades 8-10.

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