Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 1 - Tools of Geometry - 1-4 Measuring Angles - Practice and Problem-Solving Exercises - Page 32: 22


$m\angle ABC=45$ $m\angle DBC=34$

Work Step by Step

Angle Addition Postulate: $m\angle ABC + m\angle DBC =m\angle ABD$ Substitute the given values. $(8x-3)+(5x+4)=79$ Solve for x. Combine like values. $13x+1=79$ Subtract 1 from each side. $13x+1-1=79-1$ $13x=78$ Divide each side by 13. $13x\div13=78\div13$ $x=6$ Substitute for x to find $m\angle ABC$ $m\angle ABC=8x-3=8(6)-3=48-3=45$ Substitute for x to find $m\angle DBC$ $m\angle DBC=5x+4=5(6)+4=30+4=34$
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