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: 12


$m \angle A = 80^{\circ}$ $m \angle B = 100^{\circ}$ $m \angle C = 80^{\circ}$ $m\angle D = 100^{\circ}$

Work Step by Step

The sum of any two adjacent angles of a parallelogram is $180^{\circ}$ We can find the value of $x$: $m \angle A + m \angle B = 180^{\circ}$ $\frac{2x}{5} + \frac{x}{2} = 180^{\circ}$ $\frac{4x}{10} + \frac{5x}{10} = 180^{\circ}$ $\frac{9x}{10} = 180^{\circ}$ $9x = 1800^{\circ}$ $x = 200^{\circ}$ We can find the measure of $\angle A$: $m \angle A = \frac{2x}{5} = \frac{(2)(200^{\circ})}{5} = 80^{\circ}$ We can find the measure of $\angle B$: $m \angle B = \frac{x}{2} = \frac{200^{\circ}}{2} = 100^{\circ}$ Opposite angles in a parallelogram have the same measure. We can find the measure of $\angle C$: $m \angle C = m \angle A = 80^{\circ}$ We can find the measure of $\angle D$: $m\angle D = m \angle B = 100^{\circ}$
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