Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 4 - Section 4.1 - Properties of a Parallelogram - Exercises - Page 176: 3c



Work Step by Step

A parallelogram consists of two pairs of parallel sides. This gives it the property that opposite sides and angles are of equal length and size, respectively. It is also a rule that the internal angles of a parallelogram (or any four-sided shape) adds up to 360$^{\circ}$. Therefore, if we know that, because they are opposite each other, m$\angle$Q = m$\angle$N and m$\angle$M = m$\angle$P. It is given that m$\angle$M = 110$^{\circ}$, therefore m$\angle$P = 110$^{\circ}$. Out of the 360$^{\circ}$ in the parallelogram, this leaves 140$^{\circ}$ between m$\angle$Q and m$\angle$N, which are the same size, therefore are both 70$^{\circ}$.
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