find the value of the variable

When we have an angle formed by a tangent to a circle and a secant cutting the circle, the angle formed = (1/2)(measure of the of the difference of the intercepted arcs)

So...we have  x = (1/2) (160 -68) = (1/2)(92) = 46 degrees.....

I'll see if I remember how to prove this..........If I do, I'll include it a little later.......unless someone else beats me to it !!!

Well well well i cant help you in general i dont think anyone can.....

Let CG be a tangent to the circle and CE be a secant cutting the circle

angle EDG = (1/2)arc DBE

angle CED = angle FED = (1/2) minor arc FD

angle EDG = angle CED + angle ECD

angle ECD = angle EDG - angle CED

angle ECD = (1/2)arc DBE - (1/2) minor arc FD

angle ECD = (1/2) (arc DBE - minor arc FD)