Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 1 - Section 1.4 - Relationships: Perpendicular Lines - Exercises - Page 62: 30

Answer

The sum of the angles 1 and 4 must be $90^{\circ}$. By definition, this means that angles 1 and 4 are complementary.

Work Step by Step

Since AB is a straight line, the angle $\angle AOB$ is equal to $180^{\circ}$ When $\angle AOB$ is subdivided into a certain number of angles, the sum of these angles must be $180^{\circ}$ Since angles 2 and 3 are complementary, the sum of these two angles is $90^{\circ}$ Then the sum of the angles 1 and 4 must also be $90^{\circ}$. By definition, this means that angles 1 and 4 are complementary.
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