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 - Page 39: 39


Both are correct.

Work Step by Step

The definition of an angle bisector tells us that: $m\angle ABX=m\angle CBX$ The angle addition postulate tells us that: $m\angle ABX+m\angle CBX=m\angle ABC$ Substitute: $m\angle ABX+m\angle ABX=m\angle ABC$ Combine like terms: $2m\angle ABX=m\angle ABC\longrightarrow$ one student is correct Divide each side by 2: $2m\angle ABX\div2=m\angle ABC\div2$ $m\angle ABX=\frac{1}{2}m\angle ABC\longrightarrow$ the other student is also correct
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