Two complementary angles differ by 12°, find the angles?

Let the two complementary angles be
𝑥
x and
𝑦
y. According to the definition of complementary angles, the sum of the two angles is 90°:

x + y = 90° ----(1)

It is also given that the two angles differ by 12°:

x - y = 12° ----(2)

Now, we have two equations:

x + y = 90°
x - y = 12°
To solve this system of equations, we can add both equations together:

(x + y) + (x - y) = 90° + 12°

Simplifying:

2x = 102°

Now, divide both sides by 2:

x = 51°

Now, substitute the value of
𝑥
x into equation (1):

51° + y = 90°

Solve for
𝑦
y:

y = 90° - 51° = 39°

So, the two complementary angles are:

x = 51° and y = 39°