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: 29

Answer

$x=11$ $m\angle ABC=56$

Work Step by Step

Use the definition of a bisector: $m\angle ABD=m\angle CBD$ $4x-16=2x+6$ Subtract 2x from each side: $4x-16-2x=2x+6-2x$ $2x-16=6$ Add 16 to each side: $2x-16+16=6+16$ $2x=22$ Divide each side by 2: $2x\div2=22\div2$ $x=11$ Angle Addition Postulate: $m\angle ABC=(4x-16)+(2x+6)=6x-10=6(11)-10=66-10=56$
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