Elementary Geometry for College Students (5th Edition)

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

Chapter 2 - Section 2.1 - The Parallel Postulate and Special Angles - Exercises - Page 80: 24

Answer

m$\angle$ACD = 96$^{\circ}$

Work Step by Step

First, let's use the given hint and change our given diagram accordingly. Now we have line c parallel to lines a and d. Let's also create point R above point C on line c, to make labeling angles easier. Next, we can use some of the properties of parallel lines to help us. We know $\angle$BAC is congruent to $\angle$RCA because alternate interior angles are congruent. m$\angle$BAC=42$^{\circ}$, and congruent angles have the same measure, so m$\angle$RCA=42$^{\circ}$ as well. Using the same property, $\angle$EDC is congruent to $\angle$DCR. Therefore, both have a measure of 54$^{\circ}$. Using the angle addition postulate, m$\angle$RCA + m$\angle$RCD = m$\angle$ACD. Using substitution, 42$^{\circ}$+54$^{\circ}$ = m$\angle$ACD. Therefore, m$\angle$ACD = 96$^{\circ}$
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