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: 10


$m \angle 1 = 26^{\circ}$ $m \angle 2 = 128^{\circ}$ $m \angle 3 = 128^{\circ}$

Work Step by Step

Diagonals of rhombuses bisect pairs of opposite angles, so if we double $26^{\circ}$, then we will get one of the opposite angles: $m$ opposite angle = $2(26)$ Multiply to solve: $m$ opposite angle = $52$ The other opposite angle would also be bisected by that same diagonal, so $m \angle 1$ is also $26$. $\angle 2$ and $\angle 3$ are congruent but supplementary to the opposite angle that has a measure of $52^{\circ}$. $m \angle 2 = m \angle 3 = 180 - 52$ Subtract to solve: $m \angle 2 = m \angle 3 = 128$
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