Elementary Geometry for College Students (7th Edition)

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 4 - Section 4.1 - Properties of a Parallelogram - Exercises - Page 188: 11


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

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 $\angle D$: $m\angle D = m \angle B = 97^{\circ}$
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