Final answer:
To find m∠ZOY, we utilize the properties of an isosceles triangle. Since the sides ZY and EY are equal, the base angles are also equal. Subtracting the sum of the two equal angles from 180 degrees, we determine m∠ZOY to be 124 degrees.
Step-by-step explanation:
To find the measure of angle m∠ZOY, given that m∠EOY is 28 degrees, and both ZY and EY are 13, we can reason that triangle EOY is isosceles with equal sides EY = ZY since both are 13 units long.
Therefore, the angles opposite these sides are equal, thus m∠EYO = m∠EYU.
Since the sum of angles in a triangle equals 180 degrees, we can calculate m∠ZOY by subtracting the given angle and the base angle from 180 degrees.
If m∠EOY is 28 degrees and m∠EYO is also 28 degrees (isosceles triangle property), the remaining angle m∠ZOY would be 180 - 28 - 28 = 124 degrees.