### 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

See similar textbooks

Related questions

Q: Sketch the points B = (-5, 0) and C= (-3, 3).

A: Given data: The first point given is B=(-5,0). The second point given is C=(-3, 3). The sketch of…

Q: 1/Ccmpkte Srist Jor Lods 1. X CaSCX y) dxdy.

Q: 3. Rectangle PQRS with P(4, 0), Q(3, -3), R(-3, -1) and S(-2, 2); translate . =-'43

A: Consider the vertices of the rectangle PQRS with P4,0, Q3,-3, R-3,-1, and S-2,2. Draw a rectangle…

Q: Find the area of the triangle formed by the lines repr

Q: Find (4x + 3x) de + C

Q: Find the distance from the point (1, −3, 6) to the x-axis.

Q: Find gcd (3084, 1424)

Q: Find the distance from the point (1,-7,-8) to the yz-plane.

Q: Find PQ. 8x – 27 4x + 33

A: We find length PQ

Q: Solve. /3 – x - 2а + 27 — — 3

Q: Find the distance of PQ P(-3, -9) and Q(12, -11)

Q: Find the rectangular coordinate of r -6rsin0.

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and…

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y=x and y=2-x…

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and…

Q: Determine the sum of the reciprocal of roots given by the quadratic equation: ?^2 + 5? − 14 = 0

Q: 5/2 30°

A: In this question, we. Will use pythagoras therom.

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} $.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Cartesian Coordinates$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.

Similar questions

Which point is located at (4,2)?
Find the distance between the points P(3, −7, 8) and Q(−10, 7, −6). Use the square root symbol '√' where needed to give an exact value for your answer. distance between P and Q 0
Calculate the distance between the points K =(-6,0) and F=(-1,8) in the coordinate plane . Round the answer to the nearest hundredth.
find the midpoint of AB if A(-3,8) and B(-7,-6).
Click on the grid, and select Edit to draw two parallelograms for #3. 3. Two different parallelograms P and Q both have an area of 20 square units. Neither parallelogram is a rectangle. On the grid, draw two parallelograms that could be P and Q.
if 15cotx=12,then find secx?
mith Exz:- yk t3 - 6yk+2 +2Ykti +36Yx=l+2