Answer
Angles (in order: 1st, 2nd, 3rd): $59^{\circ},\ 60^{\circ},\ 61^{\circ}$
Work Step by Step
From the text, we build expressions relating the angles:
$\left[\begin{array}{lll}
\text{ 1st angle, } A & = & A\\
\text{ 2nd angle, } B & = & A+1\\
\text{ 3rd angle, } C & = & A+2
\end{array}\right.$
$ A+B+C=180^{\circ}\qquad$... sum of angles is $180^{\circ}$
... replace B and C with corresponding expressions
$ A+(A+1)+(A+2)=180\qquad$... solve for $A$
$3A+3^{\circ}=180^{\circ}$
$3A=177^{\circ}$
$A=59^{\circ}$
the other two angles are: $B=60^{\circ},\ C= 61^{\circ}.$
Angles (in order: 1st, 2nd, 3rd): $59^{\circ},\ 60^{\circ},\ 61^{\circ}$
