Chapter 4.1, Problem 12E

### 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 5 , and m ∠ B = x 2 , find the measure ofeach angle of. ▱ A B C D .

To determine

To find:

The measure of each angle of ABCD.

Explanation

Given:

Given that Given that mâˆ A=2x5, and mâˆ B=x2, 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.

Description:

In the given parallelogram ABCD, given that Given that mâˆ A=2x5, and mâˆ B=x2.

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=2x5, and mâˆ B=x2 in mâˆ A+mâˆ B=180Â°

2x5+x2=180Â°

4x+5x10=180Â°

9x10=180Â°

x=180

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