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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![## Problem 15: Solve for \( x \).
### Problem Statement:
You are given a quadrilateral with the internal angles defined algebraically. The four angles are denoted as follows:
1. Top-left angle: \( (10x + 6)^\circ \)
2. Bottom-left angle: \( (13x - 2)^\circ \)
3. Bottom-right angle: \( (8x - 1)^\circ \)
4. Top-right angle: \( 71^\circ \)
### Task:
Solve for \( x \).
#### Explanation:
In a quadrilateral, the sum of all internal angles is always \( 360^\circ \). Therefore, you can set up the following equation using the given angles:
\[
(10x + 6)^\circ + (13x - 2)^\circ + (8x - 1)^\circ + 71^\circ = 360^\circ
\]
1. Combine like terms:
\[
10x + 13x + 8x + 6 - 2 - 1 + 71 = 360
\]
2. Simplify the equation:
\[
31x + 74 = 360
\]
3. Solve for \( x \):
\[
31x + 74 - 74 = 360 - 74 \\
31x = 286 \\
x = \frac{286}{31} \\
x = 9.23
\]
Thus, the value of \( x \) is approximately \( 9.23 \).
### Conclusion:
To solve for \( x \), you recognize that the sum of the internal angles of a quadrilateral is \( 360^\circ \) and set up an equation using the given algebraic expressions for each angle. Solving this equation gives the required value of \( x \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F32dd14b8-b2bd-44f5-a3e5-80254b1ec7f4%2F3756d709-4e50-42e8-bbc4-ef12ae78e229%2Fngoqmof_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Problem 15: Solve for \( x \).
### Problem Statement:
You are given a quadrilateral with the internal angles defined algebraically. The four angles are denoted as follows:
1. Top-left angle: \( (10x + 6)^\circ \)
2. Bottom-left angle: \( (13x - 2)^\circ \)
3. Bottom-right angle: \( (8x - 1)^\circ \)
4. Top-right angle: \( 71^\circ \)
### Task:
Solve for \( x \).
#### Explanation:
In a quadrilateral, the sum of all internal angles is always \( 360^\circ \). Therefore, you can set up the following equation using the given angles:
\[
(10x + 6)^\circ + (13x - 2)^\circ + (8x - 1)^\circ + 71^\circ = 360^\circ
\]
1. Combine like terms:
\[
10x + 13x + 8x + 6 - 2 - 1 + 71 = 360
\]
2. Simplify the equation:
\[
31x + 74 = 360
\]
3. Solve for \( x \):
\[
31x + 74 - 74 = 360 - 74 \\
31x = 286 \\
x = \frac{286}{31} \\
x = 9.23
\]
Thus, the value of \( x \) is approximately \( 9.23 \).
### Conclusion:
To solve for \( x \), you recognize that the sum of the internal angles of a quadrilateral is \( 360^\circ \) and set up an equation using the given algebraic expressions for each angle. Solving this equation gives the required value of \( x \).
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