another find the variable?

OK...I can rock and roll with that.......

The arc between the two tangents = 160

So...using your previous problem involving the difference of two arcs.....we have

50 = (1/2)(160 -x)   multiply both sides by 2

100 = 160 - x       then x = 60

Now that's the measure of the arc between the "top" tangent point and the point where the secant first intercepts the circle. So...the remaining arc in the circle =

360 - 160 - 60 = 140

And the measure of "y" = 1/2 the measure of this arc  = 70.

Is the line at the bottom supposed to be tangent to the circle or  parallel  to the other tangent??