SOLUTION: You are all so helpful, did not think I'd be back so soon. However I'm stuck on this one. The story problems always get me. In triangle ABC, the measure of angle B is 2 times

Question 29576: You are all so helpful, did not think I'd be back so soon. However I'm stuck on this one. The story problems always get me.
In triangle ABC, the measure of angle B is 2 times the measure of angle A. the measure of angle C is five degrees less than angle B. Find the measure of each angle.
All I could get was B=2A, C=B-5degrees. Do not know where to go from there, not sure how to write the equation to find B. Help Please
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
In triangle ABC, the measure of angle B is 2 times the measure of angle A. the measure of angle C is five degrees less than angle B. Find the measure of each angle.
All I could get was B=2A, C=B-5degrees. Do not know where to go from there, not sure how to write the equation to find B.
Both your equations:
B=2A ----(1) C=B-5 ----(2)
are very correct. Your thought process is fine. Congratulations.
What at the moment you have temporarily forgotten is the fact that the three angles of a triangle always add up to 180 degrees no matter who does the problem on a triangle or which part of the globe the person resides!
Just observe your two equations that you have got
(1) gives meaning for B in terms of A
And (2) gives meaning for C interms of B.But we know B in terms of A.
So we can give C also in terms of A.
How?
We substitute for B in (2)
C= B - 5
C= (2A)-5 ----(3)
So the whole thing is like this.
A is A itself, B= 2A----(1) and C=2A-5----(3)
Therefore A+B+C= 180 degrees becomes
A+(2A)+(2A-5) = 180
(A+2a+2A)-5 = 180
5A-5 =180
Dividing by 5
A-1= 36
A = 36+1 = 37
B= 2A = 2X37 = 74
C=(2A-5) =74-5 = 69
Answer: A=37 degrees,B=74 degrees and C= 69 degrees
Verification: The three angles should add up to 180 degrees and of course
37+74+69 = 180 and hence our angles are correct.
HOW MUCH TO WRITE IN THE TEST?
In triangle ABC, the measure of angle B is 2 times the measure of angle A. the measure of angle C is five degrees less than angle B. Find the measure of each angle.
Given B=2A ----(1) C=B-5 ----(2)
We have in triangle ABC,
A+B+C= 180 degrees ----(*)
Putting (1) in (2),
C=(2A)-5 ----(3)
Using (1) and (3) in (*)
A+(2A)+(2A-5) = 180
5A = 180+5
5A=185
A = 185/5 =37
A=37 in (1).
B=2A=2X37 =74
B=74 i (2)
C= B-5 = 74-5 = 69
Answer: A=37 degrees,B=74 degrees and C= 69 degrees
Verification: The three angles should add up to 180 degrees and of course
37+74+69 = 180 and hence our angles are correct.

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