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: 27

Answer

$x=5$ $m\angle ABC=50$

Work Step by Step

Use the definition of a bisector: $m\angle ABD=m\angle DBC$ $5x=3x+10$ Subtract 3x from each side. $5x-3x=3x+10-3x$ $2x=10$ Divide each side by 2. $2x\div2=10\div2$ $x=5$ Angle Addition Postulate: $m\angle ABC=5x+3x+10=8x+10=8(5)+10=40+10=50$
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