There are 2 add-ins you should download from Autodesk for Fusion 360. There’s a Sketch Checker and the Fill Gaps tools.
Sketch Checker will show where the lines don’t join. Fill Gaps will join segments.
Sketch Checker:
https://apps.autodesk.com/FUSION/en/Detail/Index?id=8050506996211430178&appLang=en&os=Win64
It should be part of the app but it’s a paid add-in. Cost you $5 I think. 
But it’s way quicker than doing the extend|trim line process.