Answer:
Explanation:
Let's begin by using the definition of complementary angles: two angles are complementary if their sum is 90 degrees. We can express the two angles as x and y, and we know that:
x + y = 90 (equation 1)
We also know that the difference between the angles is 11 degrees, which we can express as:
x - y = 11 (equation 2)
We now have two equations with two unknowns, so we can solve for x and y by adding equation 1 and equation 2, which eliminates the y term:
(x + y) + (x - y) = 90 + 11
2x = 101
x = 50.5
Now we can use equation 1 to solve for y:
x + y = 90
50.5 + y = 90
y = 39.5
Therefore, the measures of the two complementary angles are 50.5 degrees and 39.5 degrees.