die Angel
fishing rod
A device for catching fish, typically consisting of a rod, a line, and a hook.
Er saß stundenlang mit seiner Angel am Ufer und wartete auf einen Biss.
He sat for hours on the riverbank with his fishing rod, waiting for a bite.

fishing rod / hinge
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fishing rod
A device for catching fish, typically consisting of a rod, a line, and a hook.
Er saß stundenlang mit seiner Angel am Ufer und wartete auf einen Biss.
He sat for hours on the riverbank with his fishing rod, waiting for a bite.

The main meaning of 'die Angel' (fishing rod) is closely connected to the verb 'angeln' (to fish). If you know the verb, you can easily remember the noun.
Am Wochenende gehen wir oft am See angeln.
On weekends we often go fishing at the lake.
The context makes the meaning clear. Words like 'Fisch' (fish), 'See' (lake), or 'Köder' (bait) point to the fishing equipment. Words like 'Tür' (door), 'Tor' (gate), or 'Scharnier' (hinge) point to the door hinge.
Er befestigte einen neuen Köder an seiner Angel.
He attached a new bait to his fishing rod.
In the context of fishing, 'Angel' is often combined with certain verbs. Typical ones are: 'die Angel auswerfen' (to cast the fishing rod), 'mit der Angel fischen' (to fish with a rod), or 'einen Fisch an der Angel haben' (to have a fish on the line).
Geduldig warf der Fischer seine Angel immer wieder aus.
Patiently, the fisherman cast his fishing rod again and again.
The idiom 'etwas aus den Angeln heben' means to completely destroy or disrupt an existing order or system. The structure is fixed.
Die Erfindung des Internets hat viele Branchen aus den Angeln gehoben.
The invention of the internet upended many industries.
joint
'Angel' and 'Gelenk' can both mean a movable connection. In this context, 'die Angel' is the hinge on a door or gate. 'Das Gelenk' is more general and is used in technology for movable connections between two parts. Learners may confuse the words because both make movement possible. With doors, however, 'Angel' or 'Scharnier' sounds more natural. 'Gelenk' is used more for bodies or technical structures, for example with a robotic arm.

Die alte Tür hängt schief, weil eine Angel locker ist.
The old door is hanging crooked because one hinge is loose.
Das Gelenk am Klappstuhl lässt sich nicht mehr richtig bewegen.
The joint on the folding chair no longer moves properly.