Final answer:
The angle measures approximately 442.73 degrees.
Step-by-step explanation:
To solve this problem, we can start by defining the angle we are looking for as 'x'. The complement of an angle is 90 degrees minus the angle itself, and the supplement of an angle is 180 degrees minus the angle itself. So, the given equation can be written as: (3/5)(90-x) + x - 3(180-x) - 80 = 400
We can simplify the equation and solve for 'x' as follows: 54 - (3/5)x + x - 540 + 3x - 80 = 400
Combining like terms: (11/5)x - 566 = 400
Adding 566 to both sides: (11/5)x = 966
Multiplying both sides by 5/11: x = 442.7273