All segments that appear to be tangent are tangent. Find the value of x. This diagram illustrates a circle with labeled points and intersecting lines, often analyzed in geometry for various angle properties. Here is a detailed transcription and explanation:**Diagram Description:**- The circle has four key points labeled W, X, Y, and Z.- Line VW is tangent to the circle at point W.- Line XY passes through the circle, intersecting the circle at points Y and Z.- Points V and X are located outside the circle such that lines WV and XW intersect at point W, forming an angle.**Key Elements:**- $\angle WVW$ is labeled as $(15x - 8)^\circ$.- An inscribed angle, indicated by an arc, suggests the motion from point W to Z.- There is a central angle $\angle YWZ$ marked explicitly as $226^\circ$.This setup is often used to explore properties of tangents, inscribed angles, and their relationships with central angles in a circle. ### Key Concepts Highlighted:1. **Tangent and Radius Relationship:** The angle between a tangent and a radius at the point of tangency is $90^\circ$. In this scenario, point V is associated with point W, indicating an external angle at their intersection. 2. **Inscribed Angle Theorem:** Inscribed angles subtended by the same arc are equal, and an inscribed angle is half the measure of the central angle that subtends the same arc. Here, $ \angle YWZ $ is a central angle measuring $226^\circ$.3. **Angle Calculation:** The diagram shows the relationship that might be useful to set up an equation involving $ x $ to find unknown angle measures.This diagram helps to enhance understanding of how external angles, central angles, and angle measurements interact with circle properties in geometry.

Name: All segments that appear to be tangent are tangent. Find the value of
Uploaded: 2024-03-20T06:46:14.000Z
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Description: All segments that appear to be tangent are tangent. Find the value of x. This diagram illustrates a circle with labeled points and intersecting lines, often analyzed in geometry for various angle properties. Here is a detailed transcription and expl

From the given diagram, ∠YWX = arc YZW / 2 ∠YWX = 226/2 = 113 The angle of the tangent VX is 180°…

Answered: (15x - 8) * 226

Math

Geometry

(15x - 8) * 226

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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All segments that appear to be tangent are tangent. Find the value of x.

This diagram illustrates a circle with labeled points and intersecting lines, often analyzed in geometry for various angle properties. Here is a detailed transcription and explanation:

**Diagram Description:**

- The circle has four key points labeled W, X, Y, and Z.
- Line VW is tangent to the circle at point W.
- Line XY passes through the circle, intersecting the circle at points Y and Z.
- Points V and X are located outside the circle such that lines WV and XW intersect at point W, forming an angle.

**Key Elements:**

- $\angle WVW$ is labeled as $(15x - 8)^\circ$.
- An inscribed angle, indicated by an arc, suggests the motion from point W to Z.
- There is a central angle $\angle YWZ$ marked explicitly as $226^\circ$.

This setup is often used to explore properties of tangents, inscribed angles, and their relationships with central angles in a circle.

### Key Concepts Highlighted:
1. **Tangent and Radius Relationship:** The angle between a tangent and a radius at the point of tangency is $90^\circ$.
In this scenario, point V is associated with point W, indicating an external angle at their intersection.

2. **Inscribed Angle Theorem:** Inscribed angles subtended by the same arc are equal, and an inscribed angle is half the measure of the central angle that subtends the same arc.
Here, $ \angle YWZ $ is a central angle measuring $226^\circ$.

3. **Angle Calculation:** The diagram shows the relationship that might be useful to set up an equation involving $ x $ to find unknown angle measures.

This diagram helps to enhance understanding of how external angles, central angles, and angle measurements interact with circle properties in geometry.

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