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: 4c



Work Step by Step

In a parallelogram, the angles opposite from each other are of equal size and all four angles total to 360$^{\circ}$. The measure of angle M is given as 122$^{\circ}$, therefore the opposite angle, P, is also 122$^{\circ}$. This leaves 360$^{\circ}$ - 244$^{\circ}$ = 116$^{\circ}$ left between Q and N. Because Q and N are opposite from each other in the parallelogram, they have an equal size. Therefore, both angles are half of the remaining degrees, which is 58$^{\circ}$.
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