### Parallel Lines and Angle MeasuresIn the diagram provided, three lines $ m $, $ n $, and $ t $ intersect, creating eight distinct angles labeled 1 through 8.The lines are arranged as follows:- Line $ m $ and Line $ t $ are intersected by Line $ n $, forming a set of angles at each intersection.### Given Information:We need to determine the value of $ x $ that makes lines $ m $ and $ n $ parallel. Two specific angle measures are provided:- $ m \angle 4 = 5x - 17 $- $ m \angle 6 = 4x + 3 $The relationships of the angles formed suggest that if $ m $ and $ n $ are to be parallel, $ \angle 4 $ and $ \angle 6 $ are alternate interior angles. For $ m \parallel n $, these alternate interior angles must be equal.### To Find:Determine the value of $ x $ such that $ m \parallel n $.### Solution:Set $ m \angle 4 $ equal to $ m \angle 6 $:\[ 5x - 17 = 4x + 3 \]Solving for $ x $:\[ 5x - 4x - 17 = 3 \]\[ x - 17 = 3 \]\[ x = 20 \]### Conclusion:The value of $ x $ that will make lines $ m $ parallel to line $ n $ is $ \boxed{20} $.

Here, angles 4 and 6 are alternate interior angles and if alternate interior angles are equal then…

Answered: Find the value of x that makes m…

Math

Geometry

Find the value of x that makes m parallel to n when m./4 = 5x – 17 and m26= 4x + 3

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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Concept explainers

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

### Parallel Lines and Angle Measures

In the diagram provided, three lines $ m $, $ n $, and $ t $ intersect, creating eight distinct angles labeled 1 through 8.

The lines are arranged as follows:
- Line $ m $ and Line $ t $ are intersected by Line $ n $, forming a set of angles at each intersection.

### Given Information:
We need to determine the value of $ x $ that makes lines $ m $ and $ n $ parallel. Two specific angle measures are provided:
- $ m \angle 4 = 5x - 17 $
- $ m \angle 6 = 4x + 3 $

The relationships of the angles formed suggest that if $ m $ and $ n $ are to be parallel, $ \angle 4 $ and $ \angle 6 $ are alternate interior angles. For $ m \parallel n $, these alternate interior angles must be equal.

### To Find:
Determine the value of $ x $ such that $ m \parallel n $.

### Solution:
Set $ m \angle 4 $ equal to $ m \angle 6 $:

\[
5x - 17 = 4x + 3
\]

Solving for $ x $:
\[
5x - 4x - 17 = 3
\]
\[
x - 17 = 3
\]
\[
x = 20
\]

### Conclusion:
The value of $ x $ that will make lines $ m $ parallel to line $ n $ is $ \boxed{20} $.

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