Сумма углов треугольника равна 180 градусов.
\[116^{\circ} + 58^{\circ} + (3v+1)^{\circ} = 180^{\circ}\]
\[174 + 3v + 1 = 180\]
\[3v + 175 = 180\]
\[3v = 180 - 175\]
\[3v = 5\]
\[v = \frac{5}{3} = 1\frac{2}{3}^{\circ}\]
Ответ: \[v = 1\frac{2}{3}^{\circ}\]