Find the angles of a rhombus if the ratio of the angles that the diagonals form with a side is 6:9.?

In a rhombus, the diagonals bisect the internal angles.
Hence, (the smaller interior angle) : (the greater interior angle) = 6 : 9

Let 6k° and 9k° be the smaller interior angle and the greater interior angle respectively.

Sum of interior angles of a rhombus :
2 × (6k° + 9k°) = 360°
k = 12

Each of the two smaller interior angles = 6 × 12° = 72°
Each of the two greater interior angles = 9 × 12° = 108°