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
![**Geometry Standards Review**
### What is the value of x?
#### Diagram Explanation
The image shows a triangle with three angles labeled as follows:
- The top angle is marked as \( 6x + 10^\circ \).
- The bottom left angle is marked as \( x + 17^\circ \).
- The bottom right angle is marked as \( 4x - 34^\circ \).
There is an input box below the diagram labeled "x = ____" for users to input the value of \( x \).
### Solving for \( x \)
To find the value of \( x \), we use the fact that the sum of the interior angles of a triangle is always 180 degrees. Therefore, we set up the equation:
\[
(6x + 10^\circ) + (x + 17^\circ) + (4x - 34^\circ) = 180^\circ
\]
Combining like terms, we get:
\[
6x + x + 4x + 10^\circ + 17^\circ - 34^\circ = 180^\circ
\]
Simplify the terms:
\[
11x - 7^\circ = 180^\circ
\]
Add 7 degrees to both sides:
\[
11x = 187^\circ
\]
Divide both sides by 11:
\[
x = 17
\]
### Answer
The value of \( x \) is \( 17 \).
**Interactive Component**
Students can input their calculated value in the provided box to check their answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fa6fceb-41d1-4797-aaee-30a73fbc9cad%2F0e4c6830-835b-41c5-abda-a0697057c6db%2Fc1ymwkk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Geometry Standards Review**
### What is the value of x?
#### Diagram Explanation
The image shows a triangle with three angles labeled as follows:
- The top angle is marked as \( 6x + 10^\circ \).
- The bottom left angle is marked as \( x + 17^\circ \).
- The bottom right angle is marked as \( 4x - 34^\circ \).
There is an input box below the diagram labeled "x = ____" for users to input the value of \( x \).
### Solving for \( x \)
To find the value of \( x \), we use the fact that the sum of the interior angles of a triangle is always 180 degrees. Therefore, we set up the equation:
\[
(6x + 10^\circ) + (x + 17^\circ) + (4x - 34^\circ) = 180^\circ
\]
Combining like terms, we get:
\[
6x + x + 4x + 10^\circ + 17^\circ - 34^\circ = 180^\circ
\]
Simplify the terms:
\[
11x - 7^\circ = 180^\circ
\]
Add 7 degrees to both sides:
\[
11x = 187^\circ
\]
Divide both sides by 11:
\[
x = 17
\]
### Answer
The value of \( x \) is \( 17 \).
**Interactive Component**
Students can input their calculated value in the provided box to check their answer.
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