In a rhombus, an altitude from the vertex of an obtuse angle bisects the opposite side. Find the measures of the angles of the rhombus.

Due to the bisecting line, you now know that two equivalent triangles have formed from the split. Since you know that all of the angles of an equivalent triangle are of the same value, you can add up all of the angles' values together (of the two equivalent triangle) to get the measures of the angles of the rhombus. Note how a rhombus has 4 equal sides, which further justifies the measures of the angles of any rhombus.