The first step for this problem is to understand what complementary angles are. Complementary angles add up to 90 degrees. Now, we have two angles. One is 2x and the other one is 3x - 20.
The sum of these two angles should be 90 degrees since they are complementary angles. So, we write:
2x + (3x - 20) = 90
To simplify this equation, combine like terms on the left side to get:
5x - 20 = 90
Now, add 20 to both sides to isolate the x terms:
5x = 110
Now, we divide by 5 to both sides of the equation to solve for x:
x = 22
Now that we have the value for x, we plug back into our two angle expressions to find the actual angles:
Angle1 = 2x = 2 * 22 = 44 degrees
Angle2 = 3x - 20 = 3 * 22 - 20 = 66 - 20 = 46 degrees
So, the two angles are 44° and 46°.