OK, I assume that the 'blue' curves are 3D curves which pass 'through' the plane of the sketch and that the 'green' arc is the sketch, correct?
If so, is it also correct to assume that you wish the 'green' arc to start & end at the 'points' where the 'blue' curves would 'intersect' the plane of the sketch?
If so, while in the sketch task, go to...
Insert -> Curves from Curves -> Intersection Point...
...and select the 'blue' curves which pass through the plane of the sketch and hit OK. Associative points will automatically be created which you can then use to define the start & end points of your 'green' arc.
John R. Baker, P.E.
Product 'Evangelist'
Product Design Solutions
Siemens PLM Software Inc.
Industry Sector
Cypress, CA