Geometry: Common Core (15th Edition)

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

Chapter 1 - Tools of Geometry - 1-5 Exploring Angle Pairs - Practice and Problem-Solving Exercises: 30

Answer

$x=12$ $m\angle ABC=112$

Work Step by Step

Use the definition of a bisector: $m\angle ABD=m\angle CBD$ $3x+20=6x-16$ Subtract 3x from each side: $3x+20-3x=6x-16-3x$ $20=3x-16$ Add 16 to each side: $20+16=3x-16+16$ $36=3x$ Divide each side by 3: $36\div3=3x\div3$ $12=x$ Angle Addition Postulate: $m\angle ABC=(3x+20)+(6x-16)=9x+4=9(12)+4=108+4=112$
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