Supplement = 2 or more angle measures whose sum is 180° (S for Straight Line)
Complement = 2 or more angle measures whose sum is 90° (C for Corner)
Define Variables: A=angle S=supplement C=Complement
Known: a+s=180 & a+c=90
Given: s=4c+24 [Why?] >>>>> "4c" because "4 times the complement" & "+24" because "exceeds .... by 24"
To solve we need to use processes for simultaneous equations or get our equation down to a single variable.
You can rewrite the known equations as such:
a+s=180 is the same as s=180-a
a+c=90 is the same as a=90-c
We can use the rewritten known equations to substitute into the given equation.
start with s=180-a
substitute [90-c] for a in the above equation giving you
s=180 - (90-c)
distribute the negative in the above equation to give you: s=180 - 90 + c
substitute [180 - 90 + c] for s in the given equation s=4c+24 giving you:
180 - 90 + c = 4c + 24
solve for c
22=c or c=22
So if the complement of angle a is 22° then the measure of angle a is 90 - 22 or 68°
The supplement would then be 180 - 68 or 112°
you can check your work by taking 112 - 24=88÷4=22