What voltage would be measured across the 15 ohm resistor with a 10v battery?

That depends on what other components are in the same circuit
along with the 15-ohm resistor.

If there's nothing else, and the battery is connected across the 15-ohm
resistor, then when you measure the voltage across the 15-ohm resistor,
your voltmeter is also connected straight across the battery, and you read
10 volts.