Chapter 4.1, Problem 10E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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 mâˆ A=2x+3, and mâˆ C=3x-27, and the â–±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 mâˆ A=2x+3, and mâˆ C=3x-27.

As per the corollary that the opposite angles of a parallelogram are congruent, the opposite angles mâˆ A and mâˆ C are equal or mâˆ A=mâˆ C and also mâˆ B and mâˆ D are equal or mâˆ B=mâˆ D.

To find the value of x, substitute mâˆ A=2x+3, and mâˆ C=3x-27 in mâˆ A=mâˆ C

2x+3=3x-27

2x-3x=-27-3

-x=-30

x=30

To find mâˆ A, substitute xÂ =30 in mâˆ A=

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