1. Solving Problems Involving Geometry

2. Two angles are supplementary if the sum of their measures is 180°
Two angles are supplementary if the sum of their measures is 180°. The measure of the first angle is 42° less than four times the second angle. Find the measure of each angle.
We’re asked to find the measure of two angles so, …
Let F = the measure of the first angle
Let S = the measure of the second angle

3. Our first equation is: F + S = 180
Now we need to find out two relationships between the first angle and the second angle.
Two angles are supplementary if the sum of their measures is 180°.
The first angle + the second angle = 180
Our first equation is: F + S = 180

4. Our second equation is F = 4S - 42
We need one more relationship between the first angle and the second angle.
2) The measure of the first angle is 42° less than four times the second angle.
The measure of the first angle F
is =
42° less than four times the second angle 4S – 42
NOTE: than reverses the order. The 42 came first in English and comes last in algebra.
Our second equation is F = 4S - 42

5. Now we have two equations in two unknowns:
F + S = 180
F = 4S – 42
I would solve these using substitution:
4S – 42 + S = 180
5S – 42 = 180
5S = 222
S = 44.4

6. Now let’s find the measure of the first angle and check our work:
F = 4S – 42
S = 44.4
F = 4(44.4) – 42
F = – 42
F = 135.6
Now we have that the first angle has a measure of and the second angle has a measure of Does that fit the story that they’re supplementary?
= 180
180 = 180
That works! The first angle is and the second angle is 44.4