Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 4 - Section 4.3 - The Rectangle, Square, and Rhombus - Exercises - Page 195: 43


1- $ \triangle AEB$ is an equilateral so each angle is equal to $ 60^{\circ} $ And all side of equilateral are congruent and they are equal to the sides of the square ABCD. 2- in a triangle BEC is an isosceles triangle ( EB and CB are congruent ) so $ \angle CEB = \angle ECB= 2x+30= 90, x= 75 $ And the same procedure for triangle DEC. 3- in a triangle DEC, where the goal is to find $\angle DEC $ , we find that $ \angle EDC=\angle ECD= 90-75=15 $ 4- last step that since $ \triangle DEC = 15+ 15 + \angle DEC = 150 $ We conclude that $ \angle DEC= 150^{\circ} $.

Work Step by Step

m$\angle$A+m$\angle$D=180 m$\angle$D=180-58 m$\angle$D=122$^{\circ}$ m$\angle$B+m$\angle$C=180 m$\angle$B+125=180 m$\angle$B=180-125 m$\angle$B=55$^{\circ}$
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