The answer may depend upon location on earth. Near the equator, 1km is going to equal roughly 0.008 degrees (1 km / 40,000 km * 360 degrees) of latitude and longitude, but near the poles, 1km is going to equal roughly 0.008 degrees latitude, but could be many many degrees longitude. (If you're 1km away from the pole, 1km travel 'west' would bring you roughly 57 degrees of longitude west.)
But, if the API just wants degrees along a great circle as the measurement, perhaps it'd be sufficient to use (n km / 40,000 km * 360 degrees). At least, 40,000km is "good enough for me" :) more accurate numbers are available.
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