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 - Got It? - Page 30: 4


$m\angle DEC=142$ $m\angle CEF=38$

Work Step by Step

Since $\angle DEF$ is a straight angle, $m\angle DEF=180$. $m\angle DEC + m\angle CEF = m\angle DEF\longrightarrow$ Angle Addition Postulate $(11x-12)+(2x+10)=180\longrightarrow$ substitute $13x-2=180\longrightarrow$ combine like terms $13x-2+2=180+2\longrightarrow$ add 2 to each side $13x=182\longrightarrow$ simplify $13x\div13=182\div13\longrightarrow$ divide each side by 13 $x=14\longrightarrow$ simplify Substitute to find the measurements. $m\angle DEC=11x-12=11(14)-12=154-12=142$ $m\angle CEF=2x+10=2(14)+10=28+10=38$
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