   Chapter 4.1, Problem 14E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# Given that m ∠ A = 2 x + y , m ∠ B = 2 x + 3 y - 20 , and m ∠ C = 3 x - y + 16 , find the measure of each angle of . To determine

To find:

The measure of each angle of ABCD.

Explanation

Given:

Given that mA=2x+y, mB=2x+3y-20, and mC=3x-y+16, 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+y, mB=2x+3y-20, and

mC=3x-y+16.

As per the corollary that the two consecutive angles of a parallelogram are supplementary, mA+mB=180

To find the value of x, substitute mA=2x+y, mB=2x+3y-20 in

mA+mB=180

2x+y+2x+3y-20=180

4x+4y-20=180

4x+4y=180+20

4x+4y=200

x+y=50 … (1)

As per the corollary that the opposite angles of a parallelogram are congruent, mA=mC

2x+y=3x-y+16

2x+y-3x+y=16

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