keeping in mind that in a rhombus, the diagonals meet at right angles, namely all angles in the middle, are 90°.
so on the bottom triangle, we have 3 angles, (x), (3x+12) and the right-angle from the intersection of the diagonals, (90).
recall that the sum of all interior angles in a triangle is 180°, therefore,
[tex]\bf (x)+(3x+12)+(90)=180\implies 4x+102=180\implies 4x=78
\\\\\\
x=\cfrac{78}{4}\implies x=\cfrac{39}{2}\implies x=19\frac{1}{2}[/tex]
