"雨が降ってきました。"は it's starting to rain.
で表せます。
また、”窓を閉めてきます”ですが
日本語を砕いて"窓を閉めさせてください”
let me close the window
※let+人+動詞の原形：人に～させる。
ex, I am so tired. Let me sleep soon.
（ほんとに疲れたので、はよ寝せて…）
オンラインレッスン中との事なのでletを使う場合は最後に
Just a moment(second),please "ちょっと待っててください"
/I am coming back here soon. "すぐ戻ってきます”
等をつけると丁寧かもしれません。(´･ω･｀)
お役に立てれば幸いです。
It is a little windy outside and then suddenly there is a torrential downpour and the rain starts splashiong all over the window sills and making an almighty noise bto the extent that it is difficult to hear your teacher. You state:
"I'm just closing the windows. It's raining.."
外は風が強くそして急に土砂降りの雨が降ってきました。
そして強い雨が窓にたたきつけられてきて、その物凄い騒音で先生の声が聞こえにくくなってきました。
そこで次の様にいうことが出来ます。
"I'm just closing the windows. It's raining."
（雨が降ってきたので、ちょっと窓を閉めに行ってきます）
Excuse me for a moment. I left my windows open and it just started raining.
Pardon me - I'd like to close my windows because it unexpectedly started raining.
Excuse me for a moment. I left my windows open and it
unexpectedly started raining.
It's always polite to apologise for interrupting someone in
the middle of something - in this case, your English lesson.
By mentioning that you left your windows open, the teacher
will automatically assume that you need to close your windows.
Pardon me - I'd like to close my windows because it unexpectedly
started raining. Pardon me is a variation of "excuse me."
Unexpectedly means that it was unlikely to happen.
Excuse me for a moment. I left my windows open and it unexpectedly started raining.（ちょっと失礼します、窓を開けっ放しにしてあるのですが、突然雨が降ってきました）
何か（ここでは、英語のレッスン）を途中で遮るときは、謝るのが礼儀です。
「窓を開けっ放しにしてある」と言えば、窓を閉めなければならないことが先生に伝わります。
Pardon me - I'd like to close my windows because it unexpectedly started raining.（すみません、突然雨が降り出したので、窓を閉めてきたいです）
"Pardon me" は "Excuse me" の別の言い方です。
"Unexpectedly" は、それが起こる可能性が低かったことを表します。
It has just started to rain and my windows are open, I am just going to close them quickly.
One moment please, I have to close my windows as it has just started to rain.
"one moment please" is used very often in a polite way, this phrase expresses and states you'd be gone quickly but will return soon.
"let me close them" can also be used as "I am just going to close them".
"one moment please"（ちょっとお待ちください）はよく使われる丁寧な表現です。一度その場を離れてまたすぐに戻ってくるときに使われます。
"I am just going to close them"（閉めてきます）の代わりに "let me close them" も使えます。
Apologies, but i must go and close my windows due to the sudden rain
I'm going to go close the windows because it has suddenly started raining
In this situation you are best to be apologetic to the teacher as you need to go away from the lesson to shut the windows and also explain why you need to do so.
'Apologies, but i must go and close my windows due to the sudden rain'
Within this sentence you are apologising, you are stating you must go and close the windows and then stating why you must do so.
ここでは、その場をいったん離れるわけなので、謝罪をし、そしてその理由を伝えるといいでしょう。
'Apologies, but I must go and close my windows due to the sudden rain'
（ごめんなさい、突然雨が降ってきたので、窓を閉めてこないといけません）
この文では、謝罪をし、窓を閉めてこないといけないと伝え、そしてその理由も説明しています。
Can you hold on for a minute because I need to close my windows? It just started raining.
I am going to close the windows in my room because it just started raining
When you want to inform your teacher that you need to close the windows because it just started raining; then you may explain this in the following ways:
-Can you hold on for a minute because I need to close my windows? It just started raining.
-I am going to close the windows in my room because it just started raining
雨が降ってきたので窓を閉めないといけないと先生に説明するなら、次のように言えます。
-Can you hold on for a minute because I need to close my windows? It just started raining.
（少し待ってもらえますか。雨が降ってきたので窓を閉めないといけません）
-I am going to close the windows in my room because it just started raining
（雨が降ってきたので部屋の窓を閉めます）
Excuse me. It is raining and I must close my windows.
Forgive me, I must close my windows because it is raining.
By saying either excuse me or forgive me, you let the teacher know that something is going on. You can then go on to explain about the rain and your need to close the windows.
"Excuse me. It is raining and I must close my windows."
"Forgive me, I must close my windows because it is raining."
これらの"excuse me"と"forgive me"のどちらかを言う事によって
先生にちょっと何かが起こったことを知らせることが出来ます。
それに続いて雨が降ってきたので窓を閉めなくてはいけない事を説明することが出来ます。
【例】
"Excuse me. It is raining and I must close my windows."
（すみません。雨が降っているので窓を閉めなければなりません）
"Forgive me, I must close my windows because it is raining."
（すみません。雨が降っているので窓を閉めなくれはいけません）
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