Basic College Mathematics (9th Edition)

Published by Pearson
ISBN 10: 0321825535
ISBN 13: 978-0-32182-553-7

Chapter 8 - Geometry - 8.2 Angles and Their Relationships - 8.2 Exercises - Page 545: 22

Answer

$\angle$ABC = $\angle$BCD = 133$^{\circ}$ $\angle$ABE = $\angle$GCD = 47$^{\circ}$

Work Step by Step

$\angle$ABC and $\angle$BCD are congruent. This means that they have the same measure. $\angle$ABC = $\angle$BCD = 133$^{\circ}$ $\angle$ABC and $\angle$GCD are congruent angles. Therefore, they have the same measure. Since $\angle$EBC is a Straight Angle. $\angle$ABC + $\angle$ABE = 180$^{\circ}$ 180$^{\circ}$ - $\angle$ABC = $\angle$ABE 180$^{\circ}$ - 133$^{\circ}$ = $\angle$ABE 47$^{\circ}$ = $\angle$ABE Therefore $\angle$ABE = $\angle$GCD = 47$^{\circ}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.