SOLUTION: 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?
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-> SOLUTION: 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?
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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?
You can put this solution on YOUR website! 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?
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
