Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 1 - Section 1.7 - The Formal Proof of a Theorem - Exercises - Page 59: 33

Answer

1. Given 2. Definition of the supplementary angle 3. Substraction Property of Inequality 4. Addition Property of Inequality 5. Definition of an obtuse angle

Work Step by Step

1. If $\angle1$ is acute and $m\angle1=x$ then $0\lt x\lt 90$ 2. The supplementary angle of $\angle 1$ is $\angle2$ and $m\angle2=y$. Therefore $x+y=180$ 3. $-x\lt 0\lt 90-x$ (We substract $x$ from all three sides of the inequality in statement (1.)) 4. $90-x\lt 90\lt 180-x$ (We add 90 to all three sides of the inequality in statement(3.)) 5. $180-x=y$ and $90\lt 180-x\lt 180$ ( because $x$ is positive), which is the definition of an obtuse angle, we can conclude, that $\angle2$ is an obtuse angle.
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