Basic College Mathematics (10th Edition)

Published by Pearson
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Chapter 8 - Geometry - 8.2 Angles and Their Relationships - 8.2 Exercises - Page 543: 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$^{\circ}$
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