Question 313623
A straight angle is divided into three smaller angles with measures a, b, and c
such that  a : b = 3 : 4   c : b = 2 : 1 What is the degree measure of the largest
angle?

{{{a/b=3/4}}}
{{{c/b=1/2}}}

cross multiply each proportion:
4a=3b
2c=b

put the two equations in a more standard form:
4a-3b+0c=0
0a-b+2c=0

since there are three variables you must have three equations. The third equation is:
a+b+c=180

Solve two equations at a time. I'll start with the first and last:

4a-3b+0c=0----------------------------------------->4a-3b+0c=0
a+b+c=180------>multiply by 3 to eliminate the b--->3a+3b+3c=540

Now add down--------------------------------------->7a+___3c=540

Next, use two different equations and eliminate b.
0a-b+2c=0
a+b+c=180

add down:
a+___3c=180


use the two new equations: 7a+3c=540------------------->  7a+3c=540
--------------------------->a+3c=180-->multipy by -1----> -a-3c=-180

add down------------------------------------------------->6a=360
solve for a----------------------------------------------->a=60

Substitute 60 for a in one of the original equations:

4a=3b
4(60)=3b
240=3b

divide by 3:   80=b

So far we know that a=60 and b=80

substitute 80 for b in one of the original equations:

2c=b
2c=80

solve for c

c=40

solution: a=60, b=80, c=40