Answer
Angles (in order: 1st, 2nd, 3rd): $129^{\circ},\ 43^{\circ},\ 8^{\circ}$
Work Step by Step
From the text, we build expressions relating the angles:
$\left[\begin{array}{lll}
\text{ 1st angle, } A & = & 3B\\
\text{ 2nd angle, } B & = & B\\
\text{ 3rd angle, } C & = & B-35^{\circ}
\end{array}\right.$
$ A+B+C=180^{\circ}\qquad$... sum of angles is $180^{\circ}$
... replace A and C with corresponding expressions
$ 3B+B+B-35^{\circ}=180^{\circ}\qquad$... solve for B
$5B-35=180^{\circ}$
$5B=215^{\circ}$
$B=43^{\circ}$
Back substitute:
$A=3B=129^{\circ}$
$C=B-35^{\circ}=8^{\circ}$
Angles (in order: 1st, 2nd, 3rd): $129^{\circ},\ 43^{\circ},\ 8^{\circ}$
