I would like to be able to change the 4 and 8 dimensions in the attached picture and have the end points follow the path/curve. An example would be to change the 4" dimension to 30 and that would force the end point to follow the curve and go past the radius so the radius would not be there anymore as shown in the example. Is this possible?
As you may be aware you can do what you want with a straight line segment but once it comes to the curves and second line segments is where trouble comes into play. Since the sketch in your image consists of three line segments and two curves the point will not transition from one segment to another.
One thing you may want to consider is placing a second point on the angled line and when you extend past the horizontal line use it to control your angle line segment and use the hidden line shown to split the line and then change the new segment and the arc and horizontal line to a construction line.