SOLUTION: If triangle ABC angle B is 8Degrees less than one half of angle A and angle C is 28 degress larger than angle A. Find the measues of the three angles of the triangle.

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Question 177875: If triangle ABC angle B is 8Degrees less than one half of angle A and angle C is 28 degress larger than angle A. Find the measues of the three angles of the triangle.
Found 2 solutions by Mathtut, solver91311:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
let a,b,and c be the measure of angle A, B, and C,respectively
:
b=(1/2)a-8....eq 1
c=a+28........eq 2
a+b+c=180.....eq 3
:
take b's value from eq 1 and c's value from eq 2 and plug them into eq 3
:
a+(a+28)+((1/2)a-8)=180....plugged in values
:
(5/2)a+20=180...collected like terms on left side
:
(5/2)a=160.....subtracted 20 from both sides
:
highlight%28a=64%29degrees......multiplied both sides by 2/5.
:
b=(1/2)a-8b=%281%2F2%29%2864%29-8=highlight%2824%29degrees
:
c=a+28c=64%2B28=highlight%2892%29degrees

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

For all triangles, the sum of measures of the interior angles is 180°. So for your triangle

But we are given that and

.

We can substitute these expressions into the sum equation thus:



Now solve for by ordinary means.

Multiply by 2:



Collect like terms:



Add -40 to both sides:



Multiply by



You should be able to figure the measures of the other two by substitution of this value.