Find mQT. 71 46 R mộT =

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Find QT

**Find \( m \overset{\frown}{QT} \).**

There is a circle with labeled points: Q, R, S, T, and X on its circumference. The center of the circle is labeled as X. Various line segments connect these points.

- \( \angle SQT \) (arc between points Q and T passing through point S) is marked as 71°.
- \( \angle QRS \) (arc between points Q and R passing through point S) is marked as 46°.

**To solve for \( m \overset{\frown}{QT} \):**

\( m \overset{\frown}{QT} = \) _______

### Explanation

This problem involves finding the measure of arc \( QT \). Here's how you can determine the solution:

1. Notice that points R, S, and Q are connected, forming a quadrilateral inside the circle.
2. Use the properties of angles and arcs in the circle for your calculations.
3. Pay attention to any inscribed angles or intercepted arcs, as they will be crucial to finding the solution.
Transcribed Image Text:**Find \( m \overset{\frown}{QT} \).** There is a circle with labeled points: Q, R, S, T, and X on its circumference. The center of the circle is labeled as X. Various line segments connect these points. - \( \angle SQT \) (arc between points Q and T passing through point S) is marked as 71°. - \( \angle QRS \) (arc between points Q and R passing through point S) is marked as 46°. **To solve for \( m \overset{\frown}{QT} \):** \( m \overset{\frown}{QT} = \) _______ ### Explanation This problem involves finding the measure of arc \( QT \). Here's how you can determine the solution: 1. Notice that points R, S, and Q are connected, forming a quadrilateral inside the circle. 2. Use the properties of angles and arcs in the circle for your calculations. 3. Pay attention to any inscribed angles or intercepted arcs, as they will be crucial to finding the solution.
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