Geometry: Common Core (15th Edition)

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

Chapter 6 - Polygons and Quadrilaterals - Chapter Review - Page 421: 12

Answer

$m \angle 1 = 101^{\circ}$ $m \angle 2 = 79^{\circ}$ $m \angle 3 = 101^{\circ}$

Work Step by Step

Consecutive angles in a parallelogram are supplementary; therefore, $\angle 1$ and $\angle 3$ are supplementary to the angle that measures $79^{\circ}$. Let's find the measures of $\angle 1$ and $\angle 3$: $m \angle 1 = m \angle 3 = 180 - 79$ Subtract to solve: $m \angle 1 = m \angle 3 = 101^{\circ}$ Opposite angles in a parallelogram are congruent; therefore, $m \angle 2 = 79^{\circ}$.
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