#### Answer

Angles (in order: 1st, 2nd, 3rd): $58^{\circ},\ 60^{\circ}$, $62^{\circ}.$

#### Work Step by Step

From the text, we build expressions relating the angles:
$\left[\begin{array}{llll}
\text{ 1st angle, } A & = & A & \text{ ...an even number }\\
\text{ 2nd angle, } B & = & A+2 & \text{ ...next even number }\\
\text{ 3rd angle, } C & = & A+4 & \text{ ...next even number }
\end{array}\right.$
$ A+(A+2)+(A+4)=180^{\circ}\qquad$... sum of angles is $180^{\circ}$
... solve for $A$
$3A+6^{\circ}=180^{\circ}$
$3A=174^{\circ}$
$A=58^{\circ}$
the other two angles are: $B=60^{\circ},\ C= 62^{\circ}.$
Angles (in order: 1st, 2nd, 3rd): $58^{\circ},\ 60^{\circ}$, $62^{\circ}.$