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 3.3, Problem 19WE
To determine

To find: the values of x and y that makes the red lines parallel and the blue lines parallel.

Expert Solution & Answer
Check Mark

Answer to Problem 19WE

  x=35

  y=20

Explanation of Solution

Given:

The diagram:

McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 3.3, Problem 19WE , additional homework tip  1

Concept Used:

Theorem 3-5: If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.

Theorem 3-6: If two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel.

Labeling the given figure:

McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 3.3, Problem 19WE , additional homework tip  2

From the above figure, it can be observed that the angles ABC and BCD are the alternate interior angles which are formed when the lines AB¯ and CD¯ are cut by the transversal BC¯ .

Now by theorem 3-5, for the red lines AB¯ and CD¯ to be parallel, we must have that the angles ABC and BCD are congruent, that is,

  mABC=mBCD3x=105x=1053x=35

Now, it can also be observed that the angles BCE and CED are the same-side interior angles which are formed when the lines BC¯ and DE¯ are cut by the transversal CE¯ .

Now by theorem 3-6, for the blue lines BC¯ and DE¯ to be parallel, we must have that the angles BCE and CED are supplementary, that is,

  mBCE+mCED=180

Now,

  mBCE=mBCD+mDCE=105+2y

And,

  mCED=x=35

So,

  mBCE+mCED=180105+2y+35=180105+35+2y=180140+2y=180

  2y=1801402y=40y=402y=20

Chapter 3 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

Ch. 3.1 - Prob. 11CECh. 3.1 - Prob. 12CECh. 3.1 - Prob. 13CECh. 3.1 - Prob. 14CECh. 3.1 - Prob. 15CECh. 3.1 - Prob. 16CECh. 3.1 - Prob. 17CECh. 3.1 - Prob. 18CECh. 3.1 - Prob. 19CECh. 3.1 - Prob. 1WECh. 3.1 - Prob. 2WECh. 3.1 - Prob. 3WECh. 3.1 - Prob. 4WECh. 3.1 - Prob. 5WECh. 3.1 - Prob. 6WECh. 3.1 - Prob. 7WECh. 3.1 - Prob. 8WECh. 3.1 - Prob. 9WECh. 3.1 - Prob. 10WECh. 3.1 - Prob. 11WECh. 3.1 - Prob. 12WECh. 3.1 - Prob. 13WECh. 3.1 - Prob. 14WECh. 3.1 - Prob. 15WECh. 3.1 - Prob. 16WECh. 3.1 - Prob. 17WECh. 3.1 - Prob. 18WECh. 3.1 - Prob. 19WECh. 3.1 - Prob. 20WECh. 3.1 - Prob. 21WECh. 3.1 - Prob. 22WECh. 3.1 - Prob. 23WECh. 3.1 - Prob. 24WECh. 3.1 - Prob. 25WECh. 3.1 - Prob. 26WECh. 3.1 - Prob. 27WECh. 3.1 - Prob. 28WECh. 3.1 - Prob. 29WECh. 3.1 - Prob. 30WECh. 3.1 - Prob. 31WECh. 3.1 - Prob. 32WECh. 3.1 - Prob. 33WECh. 3.1 - Prob. 34WECh. 3.1 - Prob. 35WECh. 3.1 - Prob. 36WECh. 3.1 - Prob. 37WECh. 3.1 - Prob. 38WECh. 3.1 - Prob. 39WECh. 3.1 - Prob. 40WECh. 3.1 - Prob. 41WECh. 3.1 - 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Prob. 28WECh. 3.6 - Prob. 1CECh. 3.6 - Prob. 2CECh. 3.6 - Prob. 3CECh. 3.6 - Prob. 4CECh. 3.6 - Prob. 5CECh. 3.6 - Prob. 6CECh. 3.6 - Prob. 1WECh. 3.6 - Prob. 2WECh. 3.6 - Prob. 3WECh. 3.6 - Prob. 4WECh. 3.6 - Prob. 5WECh. 3.6 - Prob. 6WECh. 3.6 - Prob. 7WECh. 3.6 - Prob. 8WECh. 3.6 - Prob. 9WECh. 3.6 - Prob. 10WECh. 3.6 - Prob. 11WECh. 3.6 - Prob. 12WECh. 3.6 - Prob. 13WECh. 3.6 - Prob. 14WECh. 3.6 - Prob. 15WECh. 3.6 - Prob. 16WECh. 3.6 - Prob. 17WECh. 3.6 - Prob. 18WECh. 3.6 - Prob. 19WECh. 3.6 - Prob. 20WECh. 3.6 - Prob. 21WECh. 3.6 - Prob. 22WECh. 3.6 - Prob. 23WECh. 3.6 - Prob. 24WECh. 3.6 - Prob. 25WECh. 3.6 - Prob. 26WECh. 3.6 - Prob. 27WECh. 3.6 - Prob. 28WECh. 3.6 - Prob. 29WECh. 3.6 - Prob. 30WECh. 3.6 - Prob. 1ST2Ch. 3.6 - Prob. 2ST2Ch. 3.6 - Prob. 3ST2Ch. 3.6 - Prob. 4ST2Ch. 3.6 - Prob. 5ST2Ch. 3.6 - Prob. 6ST2Ch. 3.6 - Prob. 7ST2Ch. 3.6 - Prob. 8ST2Ch. 3.6 - Prob. 9ST2Ch. 3.6 - Prob. 10ST2Ch. 3.6 - Prob. 11ST2Ch. 3.6 - Prob. 12ST2Ch. 3.6 - Prob. 13ST2Ch. 3.6 - Prob. 14ST2Ch. 3.6 - 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