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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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