   Chapter 2.CR, Problem 6CR Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Given: A C ¯ ∥ D F ¯ A E ¯ ∥ B F ¯ m ∠ A E F = 3 y m ∠ B F E = x + 45 m ∠ F B C = 2 x + 15 Find: x and y To determine

To find:

The values of x and y.

Explanation

Given:

The given statement is,

AC¯DF¯AE¯BF¯mAEF=3ymBFE=x+45

And,

mFBC=2x+15

Figure (1)

Property:

(1) If two parallel lines are cut by a transversal, then a pair of alternate interior angles is congruent.

(2) In a triangle, the sum of all interior angles is 180°.

Calculation:

The given statement is,

AC¯DF¯AE¯BF¯mAEF=3ymBFE=x+45

And,

mFBC=2x+15.

Measure of AEF is equal to the sum of measures of 4 and 12.

mAEF=m4+m12

Substitute 3y for mAEF in the above equation.

m4+m12=3y(1)

BFE and FBC are alternate interior angles

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