Elementary Geometry for College Students (7th Edition)

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

Chapter 1 - Section 1.2 - Angles and Their Relationships - Exercises - Page 49: 47


$\angle ABC=135^{\circ}$

Work Step by Step

Since vertex $b$ measures $360^{\circ}$ and the smaller reflex angle of $\angle DBC $ measures $90^{\circ}$, the larger reflex angle of $\angle DBC$ equals $360^{\circ}-90^{\circ}=270^{\circ}$. This is bisected, meaning the resulting pieces are half that of the original. We want to find the angle measurement of one of these halves. $\frac{270}{2}^{\circ}=135^{\circ}$.
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