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High School Math Geometry Geometry, Student Edition

Describe a situation in which two parallel lines are cut by a transversal and a pair of consecutive interior angles are both supplementary and congruent.

Describe a situation in which two parallel lines are cut by a transversal and a pair of consecutive interior angles are both supplementary and congruent.

Geometry, Student Edition

Geometry, Student Edition

1st Edition

ISBN: 9780078884849

Author: McGraw-Hill, McGraw Hill

Publisher: Glencoe/McGraw-Hill School Pub Co

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Question

Chapter 3.5, Problem 43HP

To determine

Describe a situation in which two parallel lines are cut by a transversal and a pair of consecutive interior angles are both supplementary and congruent.

Expert Solution & Answer

Answer to Problem 43HP

Both the consecutive interior angles should be right angled to be both supplementary and congruent.

Explanation of Solution

Calculation :

Let the measures of two consecutive interior angles which are both supplementary and congruent be x and y .

Since they are supplementary , so :

x+y=180° ……........(1)

Since they are congruent , so :

x=y

Substitute in (1) :

x+y=180°⇒x+x=180°⇒2x=180°⇒x=180°2............[divide each side by 2]⇒x=90°⇒y=90°

So, both the consecutive interior angles should be right angled to be both supplementary and congruent.

Chapter 3.5, Problem 42HP

Chapter 3.5, Problem 44STP

Chapter 3 Solutions

Geometry, Student Edition

Ch. 3.1 - Prob. 1ACYP Ch. 3.1 - Prob. 1BCYP Ch. 3.1 - Prob. 1CCYP Ch. 3.1 - Prob. 2ACYP Ch. 3.1 - Prob. 2BCYP Ch. 3.1 - Prob. 2CCYP Ch. 3.1 - Prob. 2DCYP Ch. 3.1 - Prob. 3ACYP Ch. 3.1 - Prob. 3BCYP Ch. 3.1 - Prob. 3CCYP

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