McDougal Littell Jurgensen Geometry: Student Edition Geometry
McDougal Littell Jurgensen Geometry: Student Edition Geometry
5th Edition
ISBN: 9780395977279
Author: Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Publisher: Houghton Mifflin Company College Division
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Chapter 3.4, Problem 30WE
To determine

To find:the value of x and y

Expert Solution & Answer
Check Mark

Answer to Problem 30WE

The value of x is 8° and the value of y is 12°

Explanation of Solution

Given information:The diagram below

  McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 3.4, Problem 30WE

Concept Involved:

Set up an equation based on the fact that:

  1. Alternate interior angles are congruent
  2. Triangle Sum Theorem states that Sum of interior angles of triangle adds up to 180 degrees

Solve the system of equation using the elimination metho

Calculation: Set up an equation based on the fact that alternate interior angles are congruent

  2x+y=5xy

Get all the terms in one side of the equation by subtracting 2x and y on both sides

  2x+y-2x-y=5x-2x-yy

Combine like terms on both sides of the equation and label it as 1st equation

  3x2y=0

➧1st equation

Use the Triangle Sum theorem which states that sum of interior angle of triangle add up to give 180 degrees to set up the 2nd equation

  5x+y+2x+y+100=180

Group like terms in left side of the equation

  5x+2x+y+y+100=180

Combine like terms in left side of the equation

  7x+2y+100=180

Subtract 100 on both sides

  7x+2y+100-100=180-100

Combine like terms in both sides of the equation and label it as 2nd equation

  7x+2y=80

➧2nd equation

Add 1st and 2nd equation to eliminate the variable y3x2y=07x+2y=80_10x=80

Divide by 10 on both sides of the equation10x10=8010

Simplify fraction on both sides of the equation

  x=8

Substitute 8 for x in 1st equation

  3(8)2y=0

Simplify the left side of the equation

  242y=0

Subtract 24 on both sides of the equation

  242y-24=0-24

Combine like terms in both sides of the equation

  2y=24

Divide by -2 on both sides

  2y-2=24-2

Simplify fraction on both sides of the equation

  y=12

Conclusion:

The value of x is 8° and the value of y is 12°

Chapter 3 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

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