Theresa E. answered • 10/21/20

Certified MEd TX Educator Specializing in Math, GT, & 2E students

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