Find the value of X This image is a diagram of a circle containing an inscribed triangle. The circle has an angle labeled 170 degrees, formed by two radii and a chord of the circle. Inside the triangle, two sides are labeled as 6 (units). Key elements of the diagram include:- A circle with an inscribed triangle and a chord.- The vertex angle outside the circle is given as 170 degrees.- Two of the triangle's sides within the circle are labeled with a length of 6 units each.- There is an unknown angle, labeled as $ x $ degrees, opposite the chord of the circle.To solve for the unknown $ x $ degrees, one can use the properties of circles, triangles, and inscribed angles. In particular, knowing that the sum of angles in any triangle is 180 degrees and applying properties of the specific types of triangles formed with circles (like isosceles triangles with equal radii) can help derive $ x $. ### Understanding Circle Segment GeometryIn the image shown, we have a circle with some key geometric features, which we need to analyze to solve for the unknown angle $ x $.#### Description of the Diagram:1. **Circle:** The basic shape in the diagram is a circle.2. **Angles:** Inside the circle, there are two given angles: - An angle of **70°** at one segment of the circle. - An angle of **220°** on the opposite segment of the circle.3. **Chord:** The circle contains a chord labeled with the length **8**. Below this chord is another angle labeled as $ x $.#### Explanation and Solution:To understand and solve for $ x $, we will use the following key concepts in circle geometry:1. **Sum of Angles in a Circle:** - A full circle makes up **360°**. - The sum of all angles around a point inside a circle also adds up to **360°**.Given that one segment of the circle has an angle of 70° and the remaining segment must sum up to 360° when combined with 70°, the remaining segment angle is:\[ 360° - 220° = 140° \]This leaves the angle opposite to $ x $ as 140° since the sum of angles at a point (360°) deducts the known 220° section.2. **Using the Alternate Segment Theorem:** - According to this theorem, the angle between the tangent and the chord at the point of contact is equal to the angle in the alternate segment.However, since we don't have a tangent here, we will rely on segment geometry principles and the fact that angle measures in respective segments must add up to complete the circumference angle.Hence, the angle $ x $ (vertical opposite) should be derived from subtraction:\[ x = 360° - (70° + 220°) = 70° \]Thus, the unknown angle $ x $ is **70°**.In summary, recognizing the complementary properties of angles in a circle can help solve for unknown angles effectively. Further grasp of geometric theorems can provide deeper insights and ease in solving complex problems.

Name: Find the value of X This image is a diagram of a circle containing an
Uploaded: 2024-03-20T06:46:14.000Z
Channel: Bartleby
Description: Find the value of X This image is a diagram of a circle containing an inscribed triangle. The circle has an angle labeled 170 degrees, formed by two radii and a chord of the circle. Inside the triangle, two sides are labeled as 6 (units). Key element

Here I am attaching image so that you understand each and every step.

Answered: 170° хо 6.

Math

Geometry

170° хо 6.

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

See similar textbooks

Related questions

Q: XP(X)uTX

Q: Determine an appropriate domain of each function. Identify the independent and dependent variables A…

A: To find the domain of the function

Q: The graph shown represents the history of a person learning the material on limits and continuity.…

A: According to the given information, check all the values where the function p is discontinuous.

Q: The graph shows four different functions. jhg Which function will eventually exceed the other…

Q: Find a function £

Q: Find the domain of the function.

A: The given function is F(p)=2-p Domain of the function: The set of input values for which a function…

Q: 5. Which of the following is the inverse to the function Ax) = - 8 – 5x ? a. 1 1 8 b. d. f'x) = 5x +…

A: Given that: f(x)=-8-5x

Q: Find a formula for the inverse of the function. y = 6x3 + 5

A: Given: y=6x3+5 Interchange the variables. x=6y3+5 Subtract 5 from both sides of…

Q: Let X represent the difference between the number of heads and the number of tails when a coin is…

A: If you have any questions let me know in comment box thankyou for your question.

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.

Topic Video

Question

Find the value of X

This image is a diagram of a circle containing an inscribed triangle. The circle has an angle labeled 170 degrees, formed by two radii and a chord of the circle. Inside the triangle, two sides are labeled as 6 (units).

Key elements of the diagram include:
- A circle with an inscribed triangle and a chord.
- The vertex angle outside the circle is given as 170 degrees.
- Two of the triangle's sides within the circle are labeled with a length of 6 units each.
- There is an unknown angle, labeled as $ x $ degrees, opposite the chord of the circle.

To solve for the unknown $ x $ degrees, one can use the properties of circles, triangles, and inscribed angles. In particular, knowing that the sum of angles in any triangle is 180 degrees and applying properties of the specific types of triangles formed with circles (like isosceles triangles with equal radii) can help derive $ x $.

### Understanding Circle Segment Geometry

In the image shown, we have a circle with some key geometric features, which we need to analyze to solve for the unknown angle $ x $.

#### Description of the Diagram:
1. **Circle:** The basic shape in the diagram is a circle.
2. **Angles:** Inside the circle, there are two given angles:
- An angle of **70°** at one segment of the circle.
- An angle of **220°** on the opposite segment of the circle.
3. **Chord:** The circle contains a chord labeled with the length **8**. Below this chord is another angle labeled as $ x $.

#### Explanation and Solution:

To understand and solve for $ x $, we will use the following key concepts in circle geometry:

1. **Sum of Angles in a Circle:**
- A full circle makes up **360°**.
- The sum of all angles around a point inside a circle also adds up to **360°**.

Given that one segment of the circle has an angle of 70° and the remaining segment must sum up to 360° when combined with 70°, the remaining segment angle is:

\[ 360° - 220° = 140° \]

This leaves the angle opposite to $ x $ as 140° since the sum of angles at a point (360°) deducts the known 220° section.

2. **Using the Alternate Segment Theorem:**
- According to this theorem, the angle between the tangent and the chord at the point of contact is equal to the angle in the alternate segment.

However, since we don't have a tangent here, we will rely on segment geometry principles and the fact that angle measures in respective segments must add up to complete the circumference angle.

Hence, the angle $ x $ (vertical opposite) should be derived from subtraction:

\[ x = 360° - (70° + 220°) = 70° \]

Thus, the unknown angle $ x $ is **70°**.

In summary, recognizing the complementary properties of angles in a circle can help solve for unknown angles effectively. Further grasp of geometric theorems can provide deeper insights and ease in solving complex problems.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Angles, Arcs, and Chords and Tangents$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.