Part B-What is the measure, in degrees, of ZPQR? Enter your answer in the box. 44

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
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**Part B – What is the measure, in degrees, of ∠PQR? Enter your answer in the box. [_________]**

**Diagram Explanation:**

The diagram consists of a circle centered at point T. On the circumference of the circle, points P, Q, and R are marked. From point S, which is outside the circle, a line segment intersects the circle at point P and continues to point R. Another line segment extends from S to Q, creating an intersection at P, forming angle ∠PSQ which is marked as 44°. These line segments (SP and SQ) appear to be tangents to the circle.

The objective is to determine the measure, in degrees, of ∠PQR, which is an angle within the circle subtended by points P and R and observed from point Q.

**Steps to Solve:**
1. Understand that ∠PSQ is an exterior angle to the circle formed by the tangents SP and SQ.
2. Use the properties of tangent lines and circles to relate ∠PSQ to the internal angle ∠PQR.
3. Calculate the measure of ∠PQR using geometric principles.

Enter your answer in the provided text box on the Educational website.
Transcribed Image Text:**Part B – What is the measure, in degrees, of ∠PQR? Enter your answer in the box. [_________]** **Diagram Explanation:** The diagram consists of a circle centered at point T. On the circumference of the circle, points P, Q, and R are marked. From point S, which is outside the circle, a line segment intersects the circle at point P and continues to point R. Another line segment extends from S to Q, creating an intersection at P, forming angle ∠PSQ which is marked as 44°. These line segments (SP and SQ) appear to be tangents to the circle. The objective is to determine the measure, in degrees, of ∠PQR, which is an angle within the circle subtended by points P and R and observed from point Q. **Steps to Solve:** 1. Understand that ∠PSQ is an exterior angle to the circle formed by the tangents SP and SQ. 2. Use the properties of tangent lines and circles to relate ∠PSQ to the internal angle ∠PQR. 3. Calculate the measure of ∠PQR using geometric principles. Enter your answer in the provided text box on the Educational website.
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