Example launch.json file when it exists one .net core project and angular under the same root folder...

launch.json

{
    "version": "0.2.0",
    "configurations": [
        {
            "type": "chrome",
            "request": "launch",
            "name": "Launch Chrome against localhost",
            "url": "http://localhost:4200",
            "sourceMaps": true,
            "webRoot": "${workspaceRoot}/my-own-app"
        },
        {
            "name": ".NET Core Launch (Web API)",
            "type": "coreclr",
            "request": "launch",
            "preLaunchTask": "build",
            "program": "${workspaceRoot}/MyProjectWebApi/bin/Debug/netcoreapp1.1/MyProjectWebApi.dll",
            "args": [],
            "cwd": "${workspaceRoot}/MyProjectWebApi/",
            "externalConsole": false,
            "stopAtEntry": false
        }
    ]
}