In triangle ABC, the measure of angle A is three times that of angle B. In addition, the measure of angle C is
Favorite Answer
Let b be B
Let 2(3b)-20 be C
3b+b+2(3b)-20=180
10b=200
b=20
3b=60
2(3b)-20=100
Take each sentence and make an equation so you know what you are working with.
We know:
a+b+c=180
a=3b
c=2a-20.
So I will start with the last one because I can substitute for a.
c=2(3b)-20
6b-20=c
so now I have like terms (b) to put back into my orignal equation.
a+b+c=180
(3b)+b+6b-20=180
Simplify
10b-20=180
add 20 to each side
10b=200
divide by ten on each side
b=20
Now we can put b back into figuring out a and c…..
b=20
a=3b so therefore
a=60
c= 6b-20 6(20)-20=100
c=100
So a is 60, b is 20 and c is 100
Now to check
60+20+100=180 <--correct total
A=3b
B=B
C=2(3b)-20
so you now you gotta add ’em all up
3b + B + 2(3b) – 20 = 180 now, add up all your B’s
10b-20=180
10B = 200
B=20
A = 3B = 60
C = 2(3B)-20 = 2(60)-20 = 120-20 = 100
A = 60
B = 20
C = 100
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