Basic College Mathematics (9th Edition)

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