   Chapter 2.CR, Problem 18CR ### 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
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# Given: D C ¯ ∥ A B ¯ ∠ A ≅ ∠ C m ∠ A = 3 x + y m ∠ D = 5 x + 10 m ∠ C = 5 y + 20 Find: m ∠ B To determine

To find:

The measure of B.

Explanation

Given:

The given statement is,

DC¯AB¯ACmA=3x+ymD=5x+10

And,

mC=5y+20

Figure (1)

Property:

(1) If two parallel lines are cut by transversal, then a pair of corresponding interior angles on the same side of a transversal is supplementary.

(2) Supplementary angles add up to 180°.

Calculation:

The given statement is,

DC¯AB¯ACmA=3x+ymD=5x+10

And,

mC=5y+20

A and B are congruent angles.

So, mA=mC.

Substitute 3x+y for mA and 5y+20 for mC in the above equation.

3x+y=5y+203x+y5y=203x4y=20(1)

A and D are corresponding interior angles on the same side of a transversal.

So,

mA+mD=180

Substitute 3x+y for mA and 5x+10 for mD in the above equation

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