   Chapter 4.4, 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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# In trap. 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

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