Basic College Mathematics (9th Edition)

Published by Pearson
ISBN 10: 0321825535
ISBN 13: 978-0-32182-553-7

Chapter 8 - Geometry - 8.2 Angles and Their Relationships - 8.2 Exercises: 21

Answer

$\angle$ABC = $\angle$BCD = 42$^{\circ}$ $\angle$ECD = $\angle$ABF = 138$^{\circ}$

Work Step by Step

$\angle$ABC and $\angle$BCD are congruent angles. Therefore they have the same measure. $\angle$ABC = $\angle$BCD = 42$^{\circ}$ The sum of $\angle$ABC and $\angle$ABF = 180$^{\circ}$ due to $\angle$CBF being a Straight Angle. 180$^{\circ}$ = 42$^{\circ}$ + $\angle$ABF $\angle$ABF = 180$^{\circ}$ - 42$^{\circ}$ $\angle$ABF = 138$^{\circ}$ $\angle$ABF and $\angle$ECD are congruent angles. Therefore they have the same measure. $\angle$ECD = $\angle$ABF = 138$^{\circ}$
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