Geometry: Common Core (15th Edition)

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

Chapter 3 - Parallel and Perpendicular Lines - Chapter Test - Page 211: 4

Answer

$m \angle 1 = 65^{\circ}$ $m \angle 2 = 65^{\circ}$

Work Step by Step

If the lines are parallel and are cut by a transversal, then alternate interior angles are congruent. This means that $\angle 2$ and the angle whose measure is given are alternate interior angles; therefore, $m \angle 2 = 65^{\circ}$. $\angle 1$ is congruent to $\angle 2$ because they are vertical angles, and vertical angles are congruent; therefore, $m \angle 1$ and $m \angle 2$ are both $65^{\circ}$.
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