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Here`s a word figure.

"R" in figure isn`t pronounced in British English.

When "s" is added to make it plural, "R" is not still pronounced.

Then what about this word "bother"

It`s the same as figure

What I want to know is whether "R" is pronounced if "ed" or "ing" are added.

For example, I can`t be bothered ~~~ /

You are bothering me.
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moon7296"R" in figure isn`t pronounced in British English.
Not in RP. Speakers of some regional accents may pronounce it.
moon7296
Then what about this word "bother"

It`s the same as figure

Yes.
moon7296
What I want to know is whether "R" is pronounced if "ed" or "ing" are added.

For example, I can`t be bothered ~~~ /

You are bothering me.

"bothering" is three syllables (bo-the-ring) and the "r" is fully pronounced.

"bothered" is two syllables (bo-therd) and, in RP, there is nothing like a fully-formed "r". Depending on the speaker, the "r" might be completely absent, or there might be a faint hint of a partial "r" sound merged into the vowel. In other accents the "r" may be pronounced more fully and strongly.

Edit: I forgot to mention ... in both "figure" and "bother" (and other similar words), the "r" sound is more prominent if the next word starts with a vowel sound.
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Thanks a lot Wordy.

I though almost all the British tends to omit "R"...

you added one more thing..... "r" sound is more prominent if the next word starts with a vowel sound...

For example.... figure it out. // I suppose it sounds a bit weird if "r" in figure is not pronounced like you said..
moon7296I though almost all the British tends to omit "R"...
I guess the majority do, but not all. For example, Scottish speakers tend to pronounce a noticeable "r" at the end of such words, as do some speakers with rural accents. (If you're wanting to learn to speak British English, though, you'll certainly not go wrong if you copy the RP pronunciation and omit the "r" sounds in words like these.)
moon7296For example.... figure it out. // I suppose it sounds a bit weird if "r" in figure is not pronounced like you said..
One tends to automatically make an "r" sound to ease the transition from the last vowel in "figure" to the leading vowel in "it".