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 - Lesson Check - Page 379: 3


$m \angle 1 = 40^{\circ}$ $m \angle 2 = 90^{\circ}$ $m \angle 3 = 50^{\circ}$

Work Step by Step

The diagonals of a rhombus bisect pairs of opposite angles; therefore, $m \angle 3 = 50$. We can multiply $m \angle 3$ by $2$ to find the entire angle that was bisected by the diagonal. This angle would be $2(50)$ or $100^{\circ}$. In a parallelogram, consecutive angles are supplementary; therefore, the angle that is consecutive to this angle is $180 - 100$ or $80^{\circ}$. This angle is bisected by a diagonal, giving rise to $\angle 1$ and an unnamed angle. $m \angle 1$ would be half of $80^{\circ}$ or $40^{\circ}$. The diagonals of a rhombus bisect each other at right angles; therefore, $m \angle 2 = 90^{\circ}$.
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