Given that abcd is a rhombus, what is the value of x?

A - 19.5

Step-by-step explanation:

A Rhombus is characterized by the diagonals meeting at a right angle. Therefore, the angle in the center is 90 degrees.

If you look at the bottom triangle, you know that the angles of a triangle add up to 180 degrees. You can say that all of the angles of the triangle added to 180 are:

(3x + 12) + (x) +(90) = 180 degrees

4x + 102 = 180 degrees    combining like terms

4x + 102 - 102 = 180 - 102

4x = 78

4x/4 = 78/4

x = 19.5 degrees