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: 26

Answer

a) x=11 $m\angle FGH=30$ b) $m\angle HGI=30$ c) $m\angle FGI=60$

Work Step by Step

a) Use the definition of a bisector: $3x-3=4x-14$ Subtract 3x from each side. $3x-3-3x=4x-14-3x$ $-3=x-14$ Add 14 to each side. $-3+14=x-14+14$ $11=x$ Substitute to find the measure. $m\angle FGH=3x-3=3(11)-3=33-3=30$ b) Substitute to find the measure. $m\angle HGI=4x-14=4(11)-14=44-14=30$ c) Use the definition of a bisector: $m\angle FGI=m\angle FGH+m\angle HGI=30+30=60$
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