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: 17


$\angle(2)=55^{\circ}$ $\angle(3)=125^{\circ}$ $\angle(4)=55^{\circ}$

Work Step by Step

For $\angle(2)$, you need to know that $\angle(1)$ and $\angle(2)$ form a straight line, so they are $supplementary$, meaning they add up to $180^{\circ}$. $\angle(1)+\angle(2)=180^{\circ}$ $125^{\circ}+\angle(2)=180^{\circ}$ $\angle(2)=180^{\circ}-125^{\circ}=55^{\circ}$ $\angle(3)$ is opposite $\angle(1)$ meaning they are equal. I will prove this in a bit. $\angle(4)$ is also $supplementary$ to $\angle(1)$ so it should have the same angle measurement as $\angle(2)$. $\angle(2)$ and $\angle(4)$ are opposite, and they are equal. This is because $180^{\circ}-\angle(x)$ would give the $supplementary$ angle and $180^{\circ}-(180^{\circ}-\angle(x))$=$\angle(x)$. Therefore $\angle(3)=125^{\circ}$.
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