Chapter 4.4, 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

# 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) mâˆ A,â€Šâ€Šâ€Šmâˆ B are consecutive angles.

(ii) mâˆ B,â€Šâ€Šâ€Šmâˆ C are consecutive angles.

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

If mâˆ Aâ€Šâ€Šâ€Šâ€Šandmâˆ B are consecutive angles, then mâˆ A,+â€Šâ€Šmâˆ B=180.

Substitute, mâˆ A=x2+10 and mâˆ B=x3+50.

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

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

It becomes, 5x6=180âˆ’60=120.

Multiply both sides of the equation by 6

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