The measure of the supplement of an angle exceeds 4 times the measure of the complement by 24. Find the supplement.

Answer 1

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

and

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

90+c=4c+24

90=3c+24

66=3c

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