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
**Diagram Explanation:**
- The diagram shows two straight lines intersecting, forming an angle at the intersection point.
- One of the angles formed is given as \( 78^\circ \).
- The angles are supplementary, meaning the sum of the angles on a straight line is \( 180^\circ \).
- The angle to be found is labeled as \( x \).
**Options:**
- 34°
- 132°
- 102°
- 78°
**Solution:**
In the given diagram, the angles on a straight line add up to \( 180^\circ \). Thus, the relationship between the angles is:
\[ 78^\circ + x = 180^\circ \]
To find \( x \):
\[ x = 180^\circ - 78^\circ \]
\[ x = 102^\circ \]
**Correct Answer:**
\[ x = 102^\circ \]
**Multiple Choice Answer:**
- 102°](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F788be1f4-6041-4ab5-a347-ac65fab151c5%2F306d31ef-dff2-4ba3-bfea-1f23e68db7d7%2F4l7vj1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving for the Value of \( x \)
**Problem:**
Given the diagram, solve for the value of \( x \).
**Diagram Explanation:**
- The diagram shows two straight lines intersecting, forming an angle at the intersection point.
- One of the angles formed is given as \( 78^\circ \).
- The angles are supplementary, meaning the sum of the angles on a straight line is \( 180^\circ \).
- The angle to be found is labeled as \( x \).
**Options:**
- 34°
- 132°
- 102°
- 78°
**Solution:**
In the given diagram, the angles on a straight line add up to \( 180^\circ \). Thus, the relationship between the angles is:
\[ 78^\circ + x = 180^\circ \]
To find \( x \):
\[ x = 180^\circ - 78^\circ \]
\[ x = 102^\circ \]
**Correct Answer:**
\[ x = 102^\circ \]
**Multiple Choice Answer:**
- 102°
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