I still sometimes find it difficult, despite speaking German for decades, to distinguish between the two nouns die Gelegenheit and die Angelegenheit. In all fairness, though, the fact that prefixes like an-, be-, ver-, ent-, etc. radically alter the meanings of German words is part of what makes German difficult for English speakers.

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Let's start by stripping Gelegenheit of its -heit suffix, leaving us with the adverb/adjective gelegen:

...eine Kleinstadt für sich, gelegen entlang der schweiz-französischen Grenze.

...a small town on its own, located along the Swiss-French border.

Caption 2, Die Weltmaschine - Der LHC-Teilchenbeschleuniger

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Vor der abseits gelegenen Düne gelang ihm eine sensationelle Entdeckung:

In front of this remotely situated dune, he managed to make a sensational discovery:

Captions 22-23, Abenteuer Nordsee - Unter Riesenhaien und Tintenfischen

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Thus gelegen is usually translated as "located" or situated," though it also can mean "desired" (erwünscht) or "opportune" (günstig). When we add the suffix -heit and make it a noun, it becomes: 

Die Gelegenheit lässt sich Florian nicht entgehen.

Florian doesn't let this opportunity slip by.

Caption 18, Abenteuer Nordsee - Unter Riesenhaien und Tintenfischen

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Dann lernst du ihn auch gleich kennen bei der Gelegenheit.

Then you'll also get to know him right away on this occasion.

Caption 28, Fine - sucht einen Hammer

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Die Gelegenheit is almost always translated as "opportunity," except when preceded with the preposition bei, when it's usually translated as "occasion." On a more humorous note, just as "the facilities" are used in English as a polite euphemism for the toilet, so too is die Gelegenheit an old-fashioned euphemism in German for das WC. A perhaps overly polite way to ask where the toilet is would be Wo ist hier die Gelegenheit, bitte? 

Die Angelegenheit is, on the other hand, literally a different matter altogether: 

Die Königin war fuchsteufelswild und beschloss, die Angelegenheit jetzt selbst in die Hand zu nehmen.

The Queen was "fox devil wild" [slang: angry] and decided to take the matter into her own hands now.

Captions 55-56, Märchen - Sagenhaft - Schneewittchen

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Musste zufällig jemand den Kaiser in kaiserlichen Angelegenheiten sprechen, gaben seine Diener stets dieselbe Antwort.

Should someone need to speak to the emperor about imperial affairs, his servants always gave the same answer.

Captions 20-21, Märchen - Sagenhaft - Des Kaisers neue Kleider

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I use this mnemonic device to remember the difference between Gelegenheit and Angelegenheit:

–An "opportunity" should be easy and is thus the shorter of the two words, Gelegenheit. 

–A political affair or business matter tends to suggest difficult bureaucratic procedures and is thus the longer word Angelegenheit.

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Further Learning
Go to Yabla German to find other examples of gelegen, Gelegenheit and Angelegenheit as used in real-world context.

If a German noun ends in an "e," it's usually feminine, but there are also masculine nouns that end with "e" that require special "n" or "-en" endings in all singular non-nominative cases. To complicate things further, there are also masculine nouns not ending in "e" that require the special endings too!

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Basically, the n-declination only occurs with masculine nouns, never with feminine or neuter nouns, and only a small percentage of masculine nouns are weak. Besides the rule of masculine nouns ending with -e, there is no hard and fast rule to classify them — they just have to be learned! It's helpful to know that many are professions, animals, and nationalities. Here are a few examples of weak masculine nouns to remember that you will commonly encounter in everyday usage.

Der Junge is a weak masculine noun, which you know because of the masculine der and the -e ending. Note that the -e ending changes to -en:

Der Zauberer sah zu dem zitternden Jungen hinab.

The Sorcerer looked down at the trembling Boy.

Caption 80, Märchen - Sagenhaft - Der Zauberlehrling

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However, der Nachbar is also a weak masculine noun, despite the -r ending. Note that the -r ending changes to -rn:

Du könntest einfach zum Nachbarn gehen.

You could simply go to the neighbor.

Caption 25, Fine - sucht einen Hammer

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Der Student is a very common weak masculine noun that takes the -en ending in non-nominative singular

Ich hab' 'nen spanischen Studenten eingestellt.

I've hired a Spanish student.

Caption 22, Barbara Schöneberger - Bambi-Verleihung backstage

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Der Herr is a weak masculine noun when it's translated as "lord"

Sofort rannte er zu seinem Herrn.

Immediately, he ran to his lord.

Caption 47, Märchen - Sagenhaft - Der gestiefelte Kater

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and in its more common form as the honorific "Mr." or "Mister"

Das war eine Idee von Herrn Singer.

That was an idea of Mister Singer's.

Caption 35, Modedesignerin Nina Hollein - Floria Prinzessin von Hessen

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Further Learning
Here are some examples of weak masculine nouns requiring the -n or -en endings in non-nominative singular (all of them have the masculine article der): Architekt, Astronaut, Bär, Bauer, Diplomat, Elefant, Emigrant, Held, Idiot, Kamerad, Kandidat, Kapitalist, Kommunist, Kunde, Löwe, Mensch, Neffe, Pilot, Präsident, Rabe, Russe, Schimpanse, Schwede, and Soziologe. See if you can find some examples of them in context with -n or -en endings on Yabla German. For more reading about this topic, check out the article Tricky Masculine Nouns in German.