Answer: The angle measures 69 degrees, and its complement measures 21 degrees.
Explanation:
Let's call the measure of the angle "x" degrees.
The complement of this angle will be 90 degrees minus the angle, so the measure of the complement is (90 - x) degrees.
According to the problem, the angle's measurement is 6 degrees more than 3 times the measure of its complement. So we can write the equation:
x = 3(90 - x) + 6
Now, let's solve for x:
x = 3(90 - x) + 6
Distribute the 3 on the right side:
x = 270 - 3x + 6
Add 3x to both sides:
4x = 276
Now, divide both sides by 4 to isolate x:
x = 276 / 4
x = 69
So, the angle measures 69 degrees.
Now, we can find the measure of its complement:
Complement = 90 - x
Complement = 90 - 69
Complement = 21 degrees
The angle measures 69 degrees, and its complement measures 21 degrees.