   Chapter 4.1, Problem 10E 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 that m ∠ A = 2 x + 3 , and m ∠ C = 3 x - 27 , find the measure of each angle of . To determine

To find:

The measure of each angle of ABCD.

Explanation

Given:

Given that mA=2x+3, and mC=3x-27, and the ABCD as shown below.

Corollary:

1. The opposite angles of a parallelogram are congruent.

2. Two consecutive angles of a parallelogram are supplementary.

In the given parallelogram ABCD, given that mA=2x+3, and mC=3x-27.

As per the corollary that the opposite angles of a parallelogram are congruent, the opposite angles mA and mC are equal or mA=mC and also mB and mD are equal or mB=mD.

To find the value of x, substitute mA=2x+3, and mC=3x-27 in mA=mC

2x+3=3x-27

2x-3x=-27-3

-x=-30

x=30

To find mA, substitute x =30 in mA=

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