Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 6 - Polygons and Quadrilaterals - 6-4 Properties of Rhombuses, Rectangles, and Squares - Practice and Problem-Solving Exercises - Page 379: 11


$m \angle 1 = 118^{\circ}$ $m \angle 2 = 31^{\circ}$ $m \angle 3 = 31^{\circ}$

Work Step by Step

In parallelograms, opposite angles are congruent; therefore, $m \angle 1$ is $118^{\circ}$. In parallelograms, consecutive angles are supplementary, so $\angle 2$ and $\angle 3$ are half of one of the consecutive angles. If we find the measure of a consecutive angle, we can find the measure of both $\angle 2$ and $\angle 3$. Let's find the measure of one of the consecutive angles: $m$ consecutive angle = $180 - 118$ Subtract to solve: $m$ consecutive angle = $62$ If we divide this consecutive angle by $2$, then we will get $m \angle 2$ and $m \angle 3$: $m \angle 2 = m \angle 3 = 62/2$ Divide to solve: $m \angle 2 = m \angle 3 = 31^{\circ}$
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.