ärgerlich
annoying
Describes a thing, circumstance, or event that causes annoyance, displeasure, or frustration.
Es ist wirklich ärgerlich, dass der Bus schon wieder zu spät kommt.
It's really annoying that the bus is late again.

annoying / annoyed
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annoying
Describes a thing, circumstance, or event that causes annoyance, displeasure, or frustration.
Es ist wirklich ärgerlich, dass der Bus schon wieder zu spät kommt.
It's really annoying that the bus is late again.

The adjective 'ärgerlich' (annoying/annoyed) belongs to the word family around 'der Ärger' (annoyance/trouble) and 'sich ärgern' (to get annoyed). All of these words describe the feeling of dissatisfaction or the cause of it.
Ich möchte keinen Ärger mit den Nachbarn.
I don't want any trouble with the neighbors.
The meaning of 'ärgerlich' (annoying/annoyed) depends on the subject of the sentence. If a person is the subject, it describes their feeling. If a thing or 'es' (it) is the subject, it describes an annoying situation.
Mein Kollege ist ärgerlich, weil sein Computer nicht funktioniert.
My colleague is annoyed because his computer isn't working.
To describe an annoying situation, the impersonal structure 'Es ist ärgerlich, dass ...' (It is annoying that ...) or 'Es ist ärgerlich, wenn ...' (It is annoying when ...) is often used.
Es ist ärgerlich, dass ich meinen Schlüssel vergessen habe.
It's annoying that I forgot my key.
When a person is annoyed, you use 'ärgerlich über' (annoyed about) for a thing or situation and 'ärgerlich auf' (annoyed with/at) for another person.
Sie ist ärgerlich über den Lärm.
She is annoyed about the noise.
too bad
'schade' and 'ärgerlich' both describe something negative, but the feeling behind them is different. You say 'schade' when you regret something or are disappointed. 'ärgerlich' is used when something causes annoyance or a person is annoyed. If a plan does not work out, both can fit: 'schade' sounds more like regret, while 'ärgerlich' sounds more strongly like frustration. 'ärgerlich' is especially natural when someone loses time, money, or effort.

Sie ist ärgerlich, weil der Handwerker zum zweiten Mal nicht gekommen ist.
She is annoyed because the repairman has failed to come for the second time.
Für den Kurs ist es schade, dass ihr heute nicht mitlernen könnt.
It's too bad for the course that you can't study with us today.