Final answer:
The measure of each angle is x = 10.8° and y = 79.2°.
Step-by-step explanation:
Let's call one angle x and the other angle y (the complementary angle). From the given information, we can write the equation:
x = y - 68.4°
Remember that complementary angles add up to 90°. So, we can write another equation:
x + y = 90°
We can solve these equations simultaneously by substituting the value of x from the first equation into the second equation:
(y - 68.4°) + y = 90°
Simplifying the equation:
2y - 68.4° = 90°
2y = 158.4°
y = 79.2°
Substituting this value back into the first equation, we find:
x = 79.2° - 68.4° = 10.8°
Therefore, the measure of each angle is x = 10.8° and y = 79.2°.