Complement of an angle = 90° - x.
Supplement of the complement of an angle = 180 - (90 - x).
= 180 - 90 + x
= 90 + x
Supplement of the complement of an angle less the complement of an angle = (90 + x) - (90 - x)
= 90 + x - 90 + x
= 2x
Now, the quotient of the supplement of the angle and the number 3 is [tex]\frac{180-x}{3}[/tex].
It is given that supplement of the complement of an angle less the complement of an angle exceeds the quotient of the supplement of the angle and the number 3 by 73.
Therefore, 2x = [tex]\frac{180x}{3} +73[/tex]
[tex]2x=\frac{180-x+219}{3}[/tex]
Multiply both sides by 3.
6x = 180 - x + 219
= 399 - x
Add x to both sides.
6x + x = 399
7x = 399
Divide both sides by 7.
x = 57
Hence, the required angle = 57°.
