Final answer:
To find the measure of angle Y, subtract the given angle X from 180 degrees.
Step-by-step explanation:
To find the measure of angle Y, we can use the fact that angles X and Y are supplementary, which means they add up to 180 degrees.
Given that angle X measures 116.89°, we can set up the equation: X + Y = 180.
Substituting the given value for angle X, we have 116.89 + Y = 180.
Solving for Y, we subtract 116.89 from both sides: Y = 180 - 116.89 = 63.11°.