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Go to one of the tyre online sellers websites - as an example, blackcircles.com - and enter your registration plate into the search engine. Only problem with that is that a lot of cars have a range of tyres they can be fitted with, so it might not help you out that much.
Have a look at the BACK of the wheel. It'll have numbers on it - something like 9J*19, or 19*9J. The 'J' number is the width of the wheel - which helps to define the range of widths of tyre that can be fitted to it.
Also, have a look at the drivers side door 'slam panel'. Usually a label on there with tyre sizes and pressure recommendations.
Finally, quite a few BMWs (and other makes) can have different tyre sizes on the front, compared to the back, so there may be nothing at all wrong. After all, you can only carry one spare, so if it has to go on the 'wrong' axle, then you just need to get the puncture fixed quickly so that you can go back to being properly set up.
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