Elementary Geometry for College Students (5th Edition)

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

Chapter 1 - Test - Page 69: 23

Answer

m$\angle$ABC = 108$^{\circ}$

Work Step by Step

Ray BD bisects $\angle$ABC, and rays BE and BF trisect $\angle$ABC Given m$\angle$EBD = 18$^{\circ}$, we can conclude m$\angle$FBD is also equal to 18$^{\circ}$ m$\angle$EBF = m$\angle$FBD + m$\angle$EBD. Using substitution, m$\angle$EBF = 36$^{\circ}$ Since $\angle$EBF trisects $\angle$ABC, m$\angle$ABC = 3 * m$\angle$EBF Using substitution, m$\angle$ABC = 3 * (36) Finally, after simplifying the above statement, m$\angle$ABC = 108$^{\circ}$
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