Chapter 4.1, Problem 45E

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

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 mâˆ A=x+16, mâˆ B=2(x+1), mâˆ C=32x-11, and mâˆ D=73x-16.

Definition:

The total angle in a quadrilateral is 3600.

Calculation:

In the quadrilateral ABCD, given that the diagonals mâˆ A=x+16, mâˆ B=2(x+1),

mâˆ C=32x-11, and mâˆ D=73x-16.

As per the definition, mâˆ A+mâˆ B+mâˆ C+mâˆ D=360.

Substituting mâˆ A=x+16, mâˆ B=2(x+1), mâˆ C=32x-11, and mâˆ D=73x-16 in mâˆ A+mâˆ B+mâˆ C+mâˆ D=360

x+16+Â 2x+1+32x-11+73x-16=360

x+16+Â 2x+2+32x-11+73x-16=360

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

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

18x+9x+14x6=369

41x6=369

x=369Ã—641

x=9Ã—6=54

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