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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![**Error Analysis: Describe the error in finding the angle measure.**
In this example, the given problem shows an angle \( \angle{1} \) intercepted by arcs of 122° and 70°. The calculation shown in the diagram is:
\[
m \angle{1} = 122° - 70° = 52°
\]
\[
\text{So, } m \angle{1} = 52°
\]
This is incorrect. Here is the proper way to approach the problem:
1. **Error Identification:**
- The difference was not multiplied by \( \frac{1}{2} \).
2. **Explanation:**
- To find the measure of the angle formed by two intersecting lines that intercept arcs in a circle, you must take the difference of the measures of the intercepted arcs and then multiply by \( \frac{1}{2} \).
3. **The Correct Formula:**
\[
m \angle{1} = \frac{1}{2} ( \text{difference of intercepted arcs} )
\]
Given the intercepted arcs of 122° and 70°:
\[
\text{Difference} = 122° - 70° = 52°
\]
Now, applying the correct formula:
\[
m \angle{1} = \frac{1}{2} \cdot 52° = 26°
\]
So, the correct measure of \( \angle{1} \) is 26°.
**Correct Answer:**
\[
m \angle{1} = 26°
\]
This correction is important in solving problems related to angles formed by intersecting lines that intercept arcs in a circle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff684c5ae-c1bb-4634-93a7-b9d772de63da%2F1b3fda8d-7568-46f9-b7a6-59ca31ab78b6%2Fue8u93r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Error Analysis: Describe the error in finding the angle measure.**
In this example, the given problem shows an angle \( \angle{1} \) intercepted by arcs of 122° and 70°. The calculation shown in the diagram is:
\[
m \angle{1} = 122° - 70° = 52°
\]
\[
\text{So, } m \angle{1} = 52°
\]
This is incorrect. Here is the proper way to approach the problem:
1. **Error Identification:**
- The difference was not multiplied by \( \frac{1}{2} \).
2. **Explanation:**
- To find the measure of the angle formed by two intersecting lines that intercept arcs in a circle, you must take the difference of the measures of the intercepted arcs and then multiply by \( \frac{1}{2} \).
3. **The Correct Formula:**
\[
m \angle{1} = \frac{1}{2} ( \text{difference of intercepted arcs} )
\]
Given the intercepted arcs of 122° and 70°:
\[
\text{Difference} = 122° - 70° = 52°
\]
Now, applying the correct formula:
\[
m \angle{1} = \frac{1}{2} \cdot 52° = 26°
\]
So, the correct measure of \( \angle{1} \) is 26°.
**Correct Answer:**
\[
m \angle{1} = 26°
\]
This correction is important in solving problems related to angles formed by intersecting lines that intercept arcs in a circle.
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