Geometry: Common Core (15th Edition)

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

Chapter 1 - Tools of Geometry - 1-4 Measuring Angles - Practice and Problem-Solving Exercises - Page 32: 30



Work Step by Step

Angle Addition Postulate: $m\angle AOB+m\angle BOC+ m\angle COD=m\angle AOD$ Substitute the given values. Remember $\angle AOB\cong\angle COD$ $28+(3x-2)+28=6x$ Combine like terms. $54+3x=6x$ Subtract 3x from each side. $54+3x-3x=6x-3x$ $54=3x$ Divide each side by 3. $54\div3=3x\div3$ $18=x$ Substitute for x to find the angle measures. $m\angle BOC=3x-2=3(18)-2=54-2=52$ $m\angle AOD=6x=6(18)=108$ Check the angle measures. $28+52+28\overset?=108$ $80+28\overset?=108$ $108=108\checkmark$
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