### Geometry Problem - Circle Q#### Problem Statement:In circle $ Q $ with $ m\angle PSR = 30^\circ $, find the $ m\angle PQR $.#### Diagram Explanation:The given diagram includes:- A circle centered at point $ Q $.- Points $ P $, $ S $, and $ R $ lie on the circumference of the circle.- Line segment $ PS $ intersects $ SR $ at point $ S $.- Line segments $ PQ $ and $ QR $ connect points $ P $ and $ R $ to the center $ Q $ of the circle.#### Graph or Diagram Explanation:1. **Circle Q:** A circle is shown with point $ Q $ at its center.2. **Points on the Circumference:** Points $ P $, $ S $, and $ R $ are located on the circumference of the circle.3. **Segments and Angles:** - Segment $ PS $ from $ P $ to $ S $. - Segment $ SR $ from $ S $ to $ R $. - Angle $ \angle PSR $ is marked as $ 30^\circ $. - Segment $ PQ $ from $ P $ to the center $ Q $. - Segment $ QR $ from $ Q $ to $ R $. - The task is to find the measure of angle $ \angle PQR $.#### Interactive Element:- **Answer Box:** An input box is provided for students to submit their answer.- **Submit Answer Button:** A blue button labeled "Submit Answer" allows students to submit their response.#### Solution Explanation:1. Recognize that $ \angle PSR $ is an inscribed angle, and by the Inscribed Angle Theorem, $ \angle PSR $ subtends an arc $ PR $.2. The measure of the arc $ PR $ is twice the inscribed angle, so $ \text{arc } PR = 2 \times 30^\circ = 60^\circ $.3. Realize that $ \angle PQR $ is a central angle subtending the same arc $ PR $.4. So, the measure of $ \angle PQR $ is equal to the measure of the arc it subtends. Thus, \( m\angle PQR

Name: ### Geometry Problem - Circle Q#### Problem Statement:In circle $ Q
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Description: ### Geometry Problem - Circle Q#### Problem Statement:In circle \( Q $ with $ m\angle PSR = 30^\circ $, find the $ m\angle PQR $.#### Diagram Explanation:The given diagram includes:- A circle centered at point $ Q $.- Points $ P $, $ S $,

Answered: Image /qna-images/answer/7c64914c-664f-4a44-a2f6-bf774efac5bc.jpg

Answered: In circle Q with mZPSR = 30, find the…

Math

Geometry

In circle Q with mZPSR = 30, find the mZPQR. S Q P. R

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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Concept explainers

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.

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Question

### Geometry Problem - Circle Q

#### Problem Statement:
In circle $ Q $ with $ m\angle PSR = 30^\circ $, find the $ m\angle PQR $.

#### Diagram Explanation:
The given diagram includes:
- A circle centered at point $ Q $.
- Points $ P $, $ S $, and $ R $ lie on the circumference of the circle.
- Line segment $ PS $ intersects $ SR $ at point $ S $.
- Line segments $ PQ $ and $ QR $ connect points $ P $ and $ R $ to the center $ Q $ of the circle.

#### Graph or Diagram Explanation:
1. **Circle Q:** A circle is shown with point $ Q $ at its center.
2. **Points on the Circumference:** Points $ P $, $ S $, and $ R $ are located on the circumference of the circle.
3. **Segments and Angles:**
- Segment $ PS $ from $ P $ to $ S $.
- Segment $ SR $ from $ S $ to $ R $.
- Angle $ \angle PSR $ is marked as $ 30^\circ $.
- Segment $ PQ $ from $ P $ to the center $ Q $.
- Segment $ QR $ from $ Q $ to $ R $.
- The task is to find the measure of angle $ \angle PQR $.

#### Interactive Element:
- **Answer Box:** An input box is provided for students to submit their answer.
- **Submit Answer Button:** A blue button labeled "Submit Answer" allows students to submit their response.

#### Solution Explanation:
1. Recognize that $ \angle PSR $ is an inscribed angle, and by the Inscribed Angle Theorem, $ \angle PSR $ subtends an arc $ PR $.
2. The measure of the arc $ PR $ is twice the inscribed angle, so $ \text{arc } PR = 2 \times 30^\circ = 60^\circ $.
3. Realize that $ \angle PQR $ is a central angle subtending the same arc $ PR $.
4. So, the measure of $ \angle PQR $ is equal to the measure of the arc it subtends. Thus, \( m\angle PQR

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