   Chapter 4.1, Problem 11E 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 ∠ 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 mA=2x+3, and mB=3x-23, 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.

Calculation:

In the given parallelogram ABCD, given that mA=2x+3, and mB=3x-23.

As per the corollary that the two consecutive angles of a parallelogram are supplementary, the sum of the angles mA and mB is 180°.

To find the value of x, substitute mA=2x+3, and mB=3x-23 in,

mA+mB=180°

We have,

2x+3+3x-23=180°

5x-20=180°

5x=180°+20°

5x=200°

x=20005

x=40°

To find mA, substitute x =40 in mA=2x<

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