For reference: The figure, ABCD is a parallelogram. T and C are points of tangency. Calculate x.

My progress:

I marked the angles I could find…but the main one is missing

$triangle AEB (isosceles) implies measuredangle BAE = 80^circ~and~ measuredangle FAB = 100^circ\

FAJB (cyclic quadrilateral) implies measuredangle BJF = 80^circ~and~measuredangle GJB =100^circ\

therefore JBGI: measuredangle G = measuredangle B = 80^circ~and measuredangle I = 100^circ\

measuredangle MBE = frac{overset{LARGE{frown}}{BE}}{2} =40^circ\

measuredangle BEH = 130^circ$