   Chapter 4.1, Problem 43E ### 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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# For a quadrilateral ABCD, the measures of its angles are m ∠ A = x + 16 , m ∠ B = 2 ( x + 1 ) , m ∠ C = 3 2 x - 11 , and m ∠ D = 7 3 x - 16 . Determine the measure of each angle of ABCD and whether ABCD is a parallelogram.

To determine

The measure of each angle of ABCD and to determine ABCD is a parallelogram or not.

Explanation

Given:

For a quadrilateral ABCD, the measures of its angles are mA=x+16, mB=2(x+1), mC=32x-11, and mD=73x-16.

Definition:

The total angle in a quadrilateral is 3600.

Calculation:

In the quadrilateral ABCD, given that the diagonals mA=x+16, mB=2(x+1),

mC=32x-11, and mD=73x-16.

As per the definition, mA+mB+mC+mD=360.

Substituting mA=x+16, mB=2(x+1), mC=32x-11, and mD=73x-16 in mA+mB+mC+mD=360

x+16+ 2x+1+32x-11+73x-16=360

x+16+ 2x+2+32x-11+73x-16=360

3x+32x+73x-9=360

3x+32x+73x=360+9

18x+9x+14x6=369

41x6=369

x=369×641

x=9×6=54

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