SOLUTION: In triangle ABC, B is 15 less than two times A. If C is 3 degrees larger than B, find the three angles. a+b+c=180 b=a.a-15 c=b+3 b= (a2-15)+3 b= (

Algebra ->  Triangles -> SOLUTION: In triangle ABC, B is 15 less than two times A. If C is 3 degrees larger than B, find the three angles. a+b+c=180 b=a.a-15 c=b+3 b= (a2-15)+3 b= (      Log On


   

Question 1125493: In triangle ABC, B is 15 less than two times A. If C is 3 degrees larger than B, find the three angles.
a+b+c=180
b=a.a-15
c=b+3
b= (a2-15)+3
b= (
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
In triangle ABC, the three angles
->A%2BB%2BC=180....eq.1
if B is 15 less than two times A,we have
2A=B%2B15
A=%28B%2B15%29%2F2....eq.2

if C is 3 degrees larger than+B,we have
C=B%2B3....eq.3

go to A%2BB%2BC=180....eq.1, substitute A and C from eq.2 and eq.3
%28B%2B15%29%2F2%2BB%2BB%2B3=180..........solve or B
2%28B%2B15%29%2F2%2B2B%2B2B%2B2%2A3=180%2A2
B%2B15%2B2B%2B2B%2B6=360
5B%2B21=360
5B=360-21
5B=339
B=339%2F5
highlight%28B=67.8%29

then
A=%2867.8%2B15%29%2F2
highlight%28A=41.4%29

and
C=67.8%2B3
highlight%28C=70.8%29


check the sum:
A%2BB%2BC=180
41.4%2B67.8%2B70.8=180
180=180




Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
In triangle ABC, B is 15 less than two times A. If C is 3 degrees larger than B, find the three angles.
a+b+c=180
b=a.a-15
c=b+3
b= (a2-15)+3
b= (
Let angle A be A

Then angle B = 2A - 15

And, angle C = 2A - 15 + 3, or 2A - 12

As the 3 angles sum to 180o, we get: A + 2A - 15 + 2A - 12 = 180

5A = 207

Solve that for A, angle A's measurement.

Subtract 15 from TWICE A to get B's measurement.

Subtract 12 from TWICE A to get C's measurement.

That's it!! It's as SIMPLE as that!!