Solve the triangle. \[ A=120^{\circ}, C=35^{\circ}, c=120 \] \( B=\square^{\circ} \)

To find angle \( B \), you can use the fact that the sum of the angles in a triangle equals \( 180^\circ \). So, \[ B = 180^\circ - A - C = 180^\circ - 120^\circ - 35^\circ = 25^\circ. \] Now that we have \( B = 25^\circ \), we can use the Law of Sines to find sides \( a \) and \( b \): \[ \frac{a}{\sin A} = \frac{c}{\sin C}. \] Plugging in the known values: \[ \frac{a}{\sin(120^\circ)} = \frac{120}{\sin(35^\circ)}. \] Now calculate \( a \): \[ a = \frac{120 \cdot \sin(120^\circ)}{\sin(35^\circ)}. \] Next, find \( b \) similarly: \[ \frac{b}{\sin B} = \frac{c}{\sin C} \implies b = \frac{120 \cdot \sin(25^\circ)}{\sin(35^\circ)}. \] So the solutions are \( B = 25^\circ \), \( a \) and \( b \) calculated as shown. Have fun finding those angles!