Question 1167847
the supplement of an angle is 180 minus the angle.


the complement of an angle is 90 minus the angle.


you are given that the supplement of the angle exceeds 4 times the complement of the angle by 24.


let x represent the angle.


you get:


180 - x = 4 * (90 - x) + 24


simplify to get:


180 - x = 360 - 4x + 24


subtract 180 from both sides of the equation and add 4x to both sides of the equation to get:


-x + 4x = 360 + 24 - 180


combine like terms to get:


3x = 204


solve for x to get:


x = 204/3 = 68.


the measure of the angle is 68 degrees.
the supplement of the angle is 180 - 68 = 112 degrees
the complement of the angle is 90 - 68 = 22 degrees.


the supplement of the angle is 112 degrees.
4 times the complement of the angle + 24 degrees = 4*22 + 24 = 112 degrees.


this confirms the solution is correct.