Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 2 - Section 2.5 - Convex Polygons - Exercises - Page 100: 3

Answer

x=113$^{\circ}$ y=67$^{\circ}$ z=36$^{\circ}$

Work Step by Step

m$\angle$DEA=180-36-77 m$\angle$DEA=67$^{\circ}$ Angles x and DEA form a straight line so they are supplementary. m$\angle$x=180-67 m$\angle$x=113$^{\circ}$ Angles y and DEA are corresponding angles so they are congruent. m$\angle$y=m$\angle$DEA m$\angle$y=67$^{\circ}$ Angles D and ECB are alternate interior angles so they are supplementary. m$\angle$ECB=180-m$\angle$D m$\angle$ECB=180-77 m$\angle$ECB=103$^{\circ}$ m$\angle$z=m$\angle$ECB-m$\angle$y m$\angle$z=103-67 m$\angle$z=36$^{\circ}$
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