Question

What is the value of x

Answer 1

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,

$\bf (x)+(3x+12)+(90)=180\implies 4x+102=180\implies 4x=78 \\\\\\ x=\cfrac{78}{4}\implies x=\cfrac{39}{2}\implies x=19\frac{1}{2}$