SOLUTION: Please help me solve this word problem: The sum of all angles in a triangle is always 180 degrees. The measure of the first angle is four times the measure of the second angle.

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Question 554850: Please help me solve this word problem:
The sum of all angles in a triangle is always 180 degrees. The measure of the first angle is four times the measure of the second angle. The measure of the third angle is 78° more than the second angle. What is each angle?

Thanking you in advance,
Student Learner
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the angles be a,b, and c
given:
(1) +a+%2B+b+%2B+c+=+180+
(2) +a+=+4b+
(3) +c+=+b+%2B+78+
--------------
This is 3 equations and 3 unknowns,
so it's solvable
Substitute (2) and (3) into (1)
(1) +4b+%2B+b+%2B+b+%2B+78+=+180+
(1) +6b+=+180+-+78+
(1) +6b+=+102+
(1) +b+=+17+
and, since
(2) +a+=+4b+
(2) +a+=+4%2A17+
(2) +a+=+68+
and
(3) +c+=+b+%2B+78+
(3) +c+=+17+%2B+78+
(3) +c+=+95+
The angles are 68, 17, and 95 degrees
check:
+68+%2B+17+%2B+95+=+180+
+180+=+180+
OK