〜ましょうか
shall I…? shall we…?
Verb ます-stem + ましょうか
Sign up free to review this point on a spaced schedule.
Add か to ましょう and it becomes an offer or a suggestion: 窓を開けましょうか, "shall I open the window?"; 何を食べましょうか, "what shall we eat?"
Whether it means "shall I" or "shall we" comes from context: an offer to help is "shall I", a plan made together is "shall we".
It's the natural way to offer a hand when you notice someone struggling: 持ちましょうか, "shall I carry that?" A polite reply is お願いします ("yes, please") or 大丈夫です ("I'm fine, thanks").
Between friends it's the volitional form plus か: 持とうか.
Register: Polite. Casual: the volitional form plus か, 持とうか.
Examples
暑いですね。窓を開けましょうか。
It's hot, isn't it? Shall I open the window?
重そうですね。持ちましょうか。
That looks heavy. Shall I carry it?
何時に会いましょうか。
What time shall we meet?
お昼は何を食べましょうか。
What shall we have for lunch?
駅まで送りましょうか。
Shall I take you to the station?