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
![**Solve for x**
In the diagram, there is a triangle \( \triangle ABC \) with the following angles:
1. Angle \( CAB \) is labeled as \( 5x^\circ \).
2. Angle \( ABC \) is labeled as \( 45^\circ \).
3. Angle \( ACD \) forming a straight line is labeled \( (6x + 30)^\circ \).
The task is to solve for the value of \( x \).
**Explanation of the Diagram:**
- The triangle is labeled with points A, B, and C.
- There is a point D that forms a linear pair with point C, suggesting \( \angle ACD \) is supplementary to \( \angle ACB \).
- Since a straight line measures \( 180^\circ \), the equation can be set up as:
\[ \angle ACB + \angle ACD = 180^\circ \]
This gives us the equation:
\[ 5x + 45 + (6x + 30) = 180 \]
After simplifying, solve for \( x \):
\[ 11x + 75 = 180 \]
\[ 11x = 105 \]
\[ x = \frac{105}{11} \]
**Final Equation:**
\[ x = \frac{105}{11} \]
Enter the value of \( x \) in the provided box.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb1932883-2c5b-49a7-9cf0-01e234752a0d%2Fa4373050-189a-494b-b6ef-5c4ba24c6d87%2Fkgi9acr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solve for x**
In the diagram, there is a triangle \( \triangle ABC \) with the following angles:
1. Angle \( CAB \) is labeled as \( 5x^\circ \).
2. Angle \( ABC \) is labeled as \( 45^\circ \).
3. Angle \( ACD \) forming a straight line is labeled \( (6x + 30)^\circ \).
The task is to solve for the value of \( x \).
**Explanation of the Diagram:**
- The triangle is labeled with points A, B, and C.
- There is a point D that forms a linear pair with point C, suggesting \( \angle ACD \) is supplementary to \( \angle ACB \).
- Since a straight line measures \( 180^\circ \), the equation can be set up as:
\[ \angle ACB + \angle ACD = 180^\circ \]
This gives us the equation:
\[ 5x + 45 + (6x + 30) = 180 \]
After simplifying, solve for \( x \):
\[ 11x + 75 = 180 \]
\[ 11x = 105 \]
\[ x = \frac{105}{11} \]
**Final Equation:**
\[ x = \frac{105}{11} \]
Enter the value of \( x \) in the provided box.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning