Final answer:
The statement is false because the supplement of an angle plus the angle itself must equal 180º; thus, if the supplement is 115º, the angle is 65º.
Step-by-step explanation:
The statement "The supplement of angle Q measures 115º" is false. By definition, the supplement of an angle is what, when added to the original angle, equals 180º. If angle Q has a supplement of 115º, angle Q itself must measure 180º - 115º, which is 65º. Therefore, angle Q and its supplement would add up to 180º.