   Chapter 4.4, Problem 45E 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

In trapezoid ABCD (not shown), m ∠ A = x 2 + 10 , m ∠ B = x 3 + 50 and m ∠ C = x 5 + 50 . Find all possible values of x .

To determine

To Find:

The values of x.

Explanation

Consider the following diagram.

In a trapezoid ABCD, there are two possibilities.

(i) mA,mB are consecutive angles.

(ii) mB,mC are consecutive angles.

We know that, the consecutive angles of a trapezoid are supplementary

If mAandmB are consecutive angles, then mA,+mB=180.

Substitute, mA=x2+10 and mB=x3+50.

Therefore, x2+10+x3+50=180.

Now, 3x+2x6+60=180.

It becomes, 5x6=18060=120.

Multiply both sides of the equation by 6

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