   Chapter 2.1, Problem 7E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
1 views

# Use drawings, as needed, to answer each question.Suppose that r ∥ s . Both interior angles ( ∠ 4 and ∠ 6 ) have been bisected. Using intuition, what appears to be true of ∠ 9 formed by the bisectors? To determine

To find:

The value of m9.

Explanation

Given:

The given figure is,

rs and both interior angles (4 and 6) have been bisected.

Definition:

The pairs of angles on one side of the transversal but inside the two lines are called consecutive interior Angles. Sum of measures of consecutive interior angles is 180°.

Calculation:

Consider the given figure,

4and6 are forming consecutive interior angles. Sum of measures of consecutive interior angles is 180°.

m6+m4=180°

Since 4and6 are bisected.

12(m6+m4)=12×180°12m6+12m4=90°

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