Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 4 - Section 4.1 - Properties of a Parallelogram - Exercises - Page 176: 11

Answer

$m \angle A = 83^{\circ}$ $m \angle B = 97^{\circ}$ $m \angle C = 83^{\circ}$ $m\angle D = 97^{\circ}$

Work Step by Step

The sum of any two adjacent angles of a parallelogram is $180^{\circ}$ We can find the value of $x$: $m \angle A + m \angle B = 180^{\circ}$ $(2x+3)+ (3x-23) = 180^{\circ}$ $5x-20 = 180^{\circ}$ $5x = 200^{\circ}$ $x = 40^{\circ}$ We can find the measure of $\angle A$: $m \angle A = 2x+3 = (2)(40)+3 = 83^{\circ}$ We can find the measure of $\angle B$: $m \angle B = 3x-23 = (3)(40)-23 = 97^{\circ}$ Opposite angles in a parallelogram have the same measure. We can find the measure of $\angle C$: $m \angle C = m \angle A = 83^{\circ}$ We can find the measure of $\angle D$: $m\angle D = m \angle B = 97^{\circ}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.