Final answer:
To find the measure of the angle formed between two non-adjacent angles on a line, we subtract the sum of the two given angles from 360 degrees. But the provided answer options do not include the calculated measure of 273 degrees, suggesting a possible error in the question or answer choices.
Step-by-step explanation:
The question asks for the measure of the angle formed between two non-adjacent angles on a line, given their measurements are 24 degrees and 63 degrees, respectively. According to the Protractor Postulate, which implies that the sum of angles around a point is 360 degrees, we must subtract the sum of the two given angles from 360 degrees to find the measure of the angle between them. Therefore, the measure of the angle in question is calculated as follows:
360 degrees - (24 degrees + 63 degrees) = 360 degrees - 87 degrees = 273 degrees.
However, since the options provided (93 degrees, 87 degrees, 27 degrees, and 39 degrees) do not include 273 degrees, there seems to be a misunderstanding or mistake either in the formation of the question or the provided answer choices. None of the provided options are correct based on the given angle measurements and the Protractor Postulate.