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 - 3-2 Properties of Parallel Lines - Got It? - Page 151: 3


a) 75 b) 75 c) 105 d) 105 e) 105 f) 105

Work Step by Step

a) $\angle 4$ and the angle measuring $105^o$ are supplementary because of the same-side interior angles postulate, so $m\angle4=75$. Using the alternate interior angles theorem, we know $\angle4\cong\angle1$, so $m\angle1=75$. b) Using the vertical angles theorem, $\angle1\cong\angle2$, so $m\angle2=75$. c) The corresponding angles theorem tells us that $\angle5$ is congruent to the angle measuring $105^o$, so $m\angle5=105$ d) $\angle6$ forms an alternate interior pair with the angle that measures $105^o$. The alternate interior angles theorem tells us the pair is congruent. e) The vertical angles theorem tells us that $\angle7$ is congruent to the angle that measures $105^o$. f) $\angle8$ and $\angle1$ are supplementary because they form a linear pair. Since $m\angle1=75$, we know $m\angle8=105$.
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