Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 10 - Geometry - 10.1 Points, Lines, Planes, and Angles - Exercise Set 10.1: 26

Answer

$m\angle{1} = 47^o \\m\angle{2}=133^o \\m\angle{3} = 47^o$

Work Step by Step

The 133-degree angle and angle $2$ are vertical angles, so they have the same measurements. Thus, $m\angle{2} = 133^o$ Angles 1 and 2 are supplementary, so their sum is 180 degrees. Thus, $m\angle{1} = (180^o-m\angle{2}) \\m\angle{1} = (180-133)^o \\m\angle{1} = 47^o$ Angles 1 and 3 are vertical angles, so they have the same measurements. Thus, $m\angle{3} = m\angle{1} = 47^o$
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