Chapter 4.1, Problem 11E

### 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 ∠ B = 3 x - 23 , 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 B=3x-23, 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.

Calculation:

In the given parallelogram ABCD, given that mâˆ A=2x+3, and mâˆ B=3x-23.

As per the corollary that the two consecutive angles of a parallelogram are supplementary, the sum of the angles mâˆ A and mâˆ B is 180Â°.

To find the value of x, substitute mâˆ A=2x+3, and mâˆ B=3x-23 in,

mâˆ A+mâˆ B=180Â°

We have,

2x+3+3x-23=180Â°

5x-20=180Â°

5x=180Â°+20Â°

5x=200Â°

x=20005

x=40Â°

To find mâˆ A, substitute xÂ =40 in mâˆ A=2x<

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