Thinking Mathematically (6th Edition)

Published by Pearson

Chapter 10 - Geometry - 10.1 Points, Lines, Planes, and Angles - Exercise Set 10.1 - Page 616: 27

Answer

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

Work Step by Step

The right angle and angle 2 are vertical angles. This means that they have the same measurements. Thus, $m\angle{2} = 90^o$. The 40-degree angle and angle 1 are complementary angles, so their sum is 90 degrees. Thus, $m\angle{1}=90^o-40^o \\m\angle{1}=40^o$ Angles 1 and 3 are vertical angles, so their measurements are the same. Thus, $m\angle{3} = m\angle{1} = 50^o$

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