Given m||n, find the value of x.

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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Given m ||n , find the value of x.

**Problem Description:**

Given two parallel lines \( m \parallel n \), find the value of \( x \).

**Diagram Explanation:**

The image shows two parallel lines, \( m \) and \( n \). A transversal intersects both lines, creating alternate interior angles. 

- The angle on line \( m \) is labeled \( (x+6)^\circ \).
- The angle on line \( n \) is labeled \( (x+10)^\circ \).

**Solution:**

Since lines \( m \) and \( n \) are parallel, the alternate interior angles are equal. Therefore:

\[
(x+6)^\circ = (x+10)^\circ
\]

Solving for \( x \):

\[
x + 6 = x + 10
\]

Subtract \( x \) from both sides:
\[
6 = 10
\]

Subtract 6 from both sides:
\[
0 = 4
\]

Since the equation simplifies incorrectly, re-evaluate assumptions or check the problem setup for clarity.
Transcribed Image Text:**Problem Description:** Given two parallel lines \( m \parallel n \), find the value of \( x \). **Diagram Explanation:** The image shows two parallel lines, \( m \) and \( n \). A transversal intersects both lines, creating alternate interior angles. - The angle on line \( m \) is labeled \( (x+6)^\circ \). - The angle on line \( n \) is labeled \( (x+10)^\circ \). **Solution:** Since lines \( m \) and \( n \) are parallel, the alternate interior angles are equal. Therefore: \[ (x+6)^\circ = (x+10)^\circ \] Solving for \( x \): \[ x + 6 = x + 10 \] Subtract \( x \) from both sides: \[ 6 = 10 \] Subtract 6 from both sides: \[ 0 = 4 \] Since the equation simplifies incorrectly, re-evaluate assumptions or check the problem setup for clarity.
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