Question 1143886
see my worksheet below.
additional comments below the worksheet.


<img src = "http://theo.x10hosting.com/2019/081301.jpg" alt="###" >


reference on altitude of a rhombus can be found at <a href = "https://www.mathopenref.com/rhombus.html#targetText=The%20altitude%20of%20a%20rhombus,may%20have%20to%20be%20extended)." target = "_blank">https://www.mathopenref.com/rhombus.html#targetText=The%20altitude%20of%20a%20rhombus,may%20have%20to%20be%20extended).</a.


reference on properties of a rhombus can be found at <a href = "https://www.mbacrystalball.com/blog/2015/11/13/quadrilaterals-properties-parallelograms-trapezium-rhombus/" target = "_blank">https://www.mbacrystalball.com/blog/2015/11/13/quadrilaterals-properties-parallelograms-trapezium-rhombus/</a>


from my worksheet, DE is the altitude of rhombux ABCD.


\right triangle EAD is formed by the altitude and the closest side of the rhombus.


DE = 90 mm
AD = 120 mm


cos(EDA) = 90/120.


angle (EDA) = arccos(90/120) = 41.40962211 degrees = angle x in the diagram.


angle y in the diagram is complementary to angle x, since angle x + y = 90 degrees.


angle y is the smaller of the interior angles of rhombus ABCD.


angle y is equal to 90 minus angle x = 48.59037789 degrees.


that should be your answer as best i can determine.