Download Solving Problems Involving Geometry

Solving Problems Involving Geometry
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
Now we need to find out two relationships between the first angle and
the second angle.
1) 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
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
is
F
=
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
Now we have two equations in two unknowns:
F + S = 180
F = 4S – 42
I would solve these using substitution:
F + S = 180
F = 4S – 42
4S – 42 + S = 180
5S – 42 = 180
5S = 222
S = 44.4
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 = 177.6 – 42
F = 135.6
Now we have that the first angle has a measure of 135.6 and the second angle has
a measure of 44.4. Does that fit the story that they’re supplementary?
135.6 + 44.4 = 180
180 = 180
That works!
The first angle is 135.6 and the second angle is 44.4