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
Related questions
Question
**Description:**
- The circle has two radii, each marked as 6 units.
- There is a chord dividing the circle into two segments: one arc measuring \( 170^\circ \) and another angle \( x^\circ \) intercepting the major arc.
- The angle formed by the radii at the center of the circle is the central angle, which is \( 170^\circ \).
- The external angle subtending the arc intercepts on the circumference.
### Steps to Solution
1. **Identify Key Angles:**
- Note that the sum of the angles around the central point in a circle is \( 360^\circ \).
2. **Calculate the Missing Angle:**
- To find the value of \( x \), use the relationship between the angles in the circle.
- The angle \( x \) is the remaining angle around point, given that the full circle is \( 360^\circ \).
\[
x = 360^\circ - 170^\circ
\]
3. **Perform the Calculation:**
- Substitute the given value into the equation:
\[
x = 360^\circ - 170^\circ = 190^\circ
\]
Therefore, the value of \( x \) is \( 190^\circ \).
This solution employs the properties of circles and the sum of central angles. This understanding helps in solving various geometrical problems involving circles and angles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7c29d2f-5cf3-43f5-aa90-abc5a822140a%2Fac65eb93-4386-47f9-90b2-bef288816e9e%2Fmttthz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
Given the following circle, find the value of \( x \).
**Description:**
- The circle has two radii, each marked as 6 units.
- There is a chord dividing the circle into two segments: one arc measuring \( 170^\circ \) and another angle \( x^\circ \) intercepting the major arc.
- The angle formed by the radii at the center of the circle is the central angle, which is \( 170^\circ \).
- The external angle subtending the arc intercepts on the circumference.
### Steps to Solution
1. **Identify Key Angles:**
- Note that the sum of the angles around the central point in a circle is \( 360^\circ \).
2. **Calculate the Missing Angle:**
- To find the value of \( x \), use the relationship between the angles in the circle.
- The angle \( x \) is the remaining angle around point, given that the full circle is \( 360^\circ \).
\[
x = 360^\circ - 170^\circ
\]
3. **Perform the Calculation:**
- Substitute the given value into the equation:
\[
x = 360^\circ - 170^\circ = 190^\circ
\]
Therefore, the value of \( x \) is \( 190^\circ \).
This solution employs the properties of circles and the sum of central angles. This understanding helps in solving various geometrical problems involving circles and angles.
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