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 3.2, Problem 18WE
To determine

To find: the values of x and y .

Expert Solution & Answer
Check Mark

Answer to Problem 18WE

  x=25

  y=10

Explanation of Solution

Given:

The diagram:

McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 3.2, Problem 18WE , additional homework tip  1

Concept Used:

Theorem 3-3: If two parallel lines are cut by a transversal then the same-side interior angles are supplementary.

Label the given figure as shown below:

McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 3.2, Problem 18WE , additional homework tip  2

Now, lines AB¯CD¯ and AC¯ is a transversal, so by theorem 3-3,

  mBAC+mACD=180 (Supplementary angles)

  120+2x+y=1802x+y=1801202x+y=60

Similarly, lines CD¯EF¯ and CE¯ is a transversal, so by theorem 3-3,

  mDCE+mCEF=180 (Supplementary angles)

  2xy+140=1802xy=1801402xy=40

Now, consider the equations:

  2x+y=60 ….. (1)

  2xy=40 ….. (2)

Add equations (1) and (2),

  (2x+y)+(2xy)=60+402x+y+2xy=1002x+2x+yy=100

  4x=100x=1004x=25

Substitute x=25 in equation (1),

  2(25)+y=6050+y=60y=6050y=10

Chapter 3 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

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