VsTsc task unsupported by toolsversion
Try repairing the TypeScript Tools package - go to the Control Panel > Programs & Features, and choose "TypeScript Tools for Microsoft Visual Studio 2015 xxxx", choose Change and then in the installer click Repair.
I had this issue just now in Visual Studio 2015, after recreating a brand new ASP.NET Core project, and doing the repair fixed it.
I was using VS2015 after dumping 2013 for it's lack of integration.I got past this problem by removing a previously installed TypeScript package for VS2013.
As always, be sure to restart VS2015 after doing the uninstall.