To solve this problem, we need to understand the concept of complementary angles. Two angles are complementary when their measures add up to 90 degrees.
Let’s denote the measure of the first angle as x. According to the problem, the second angle, which is its complementary angle, can be represented as 90 – x.
The angle measures 36 less than its complementary angle, so we can set up the equation:
x = (90 – x) – 36
Now, let’s simplify this equation:
x = 90 – x – 36
x = 54 – x
Now, add x to both sides:
2x = 54
Next, divide both sides by 2:
x = 27
This means the first angle measures 27 degrees. Now, we can find the measure of the complementary angle:
90 – x = 90 – 27 = 63
So, the two angles are:
- First angle: 27 degrees
- Complementary angle: 63 degrees
In conclusion, the measures of the angles are 27 degrees and 63 degrees.