Chapter 4.CR, Problem 17CR

### 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

# Review Exercises Using the information from Review Exercise 16, determine which diagonal ( M O - or P N - ) would be longer. Exercise 16: Given: ▱ M N O P m ∠ M = 4 x m ∠ O = 2 x + 50 Find:   m ∠ M   and   m ∠ P

To determine

To Find:

The longest diagonal of the parallelogram MNOP.

Explanation

Properties Used:

1. Two consecutive angles of a parallelogram are supplementary.

2. The opposite angles of a parallelogram are congruent.

3. In a parallelogram with unequal pairs of consecutive angles, the longer diagonal lies opposite the obtuse angle.

Calculation:

It is given that MNOP is a parallelogram with mâˆ M=4x and mâˆ O=2x+50.

In the parallelogram MNOP, âˆ M and âˆ O are opposite angles.

By the property â€˜opposite angles of a parallelogram are congruentâ€™, mâˆ M=mâˆ O.

4x=2x+50

2x=50

x=25Â°

Substituting the value of x in measure of angle M,

mâˆ M=4x=425=100Â°

In the parallelogram MNOP, mâˆ M and mâˆ P are consecutive angles

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