Final answer:
To find the angle, complement, and supplement of an angle, solve the equation 2(180 - x) = 5(90 - x) - 69. The angle is 7 degrees, its complement is 83 degrees, and its supplement is 173 degrees.
Step-by-step explanation:
To solve this problem, let's first define the angle as x. The complement of the angle would be 90 - x, and the supplement of the angle would be 180 - x.
According to the problem, twice the measure of the supplement of the angle is 69 less than 5 times the measure of the complement of the angle, so we can write the equation: 2(180 - x) = 5(90 - x) - 69.
Simplifying the equation, we get: 360 - 2x = 450 - 5x - 69. Combining like terms, we have 2x - 5x = 360 - 450 + 69. Simplifying further, we get -3x = -21. Dividing both sides of the equation by -3 gives us x = 7.
So, the angle is 7 degrees, its complement is 90 - 7 = 83 degrees, and its supplement is 180 - 7 = 173 degrees.