SOLUTION: One angle of a triangle is 3 times as large as another. The measure of the third angle is 40 degrees greater than that of the smallest angle. How large are the angles?

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: One angle of a triangle is 3 times as large as another. The measure of the third angle is 40 degrees greater than that of the smallest angle. How large are the angles?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 743699: One angle of a triangle is 3 times as large as another. The measure of the third angle is 40 degrees greater than that of the smallest angle. How large are the angles?
Found 2 solutions by stanbon, davethejackal:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
One angle of a triangle is 3 times as large as another. The measure of the third angle is 40 degrees greater than that of the smallest angle. How large are the angles?
-------
Equations:
a = 3b
c = b+40
a + b + c = 180
-----
Substitute for a and for c, and solve for "b":
3b + b + b+40 = 180
5b = 140
b = 28 degrees
a = 3b = 84 degrees
c = 68 degrees
-----------------------
Cheers,
Stan H.
=====================

Answer by davethejackal(28) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a%5B1%5D+, +a%5B2%5D+ and +a%5B3%5D+ be the angles in the triangle

Total angles in a triangle always add up to 180 so
+a%5B1%5D%2Ba%5B2%5D%2Ba%5B3%5D=180+ [1]

"One angle of a triangle is 3 times as large as another"
+a%5B1%5D=3a%5B3%5D+ [2]

"The measure of the third angle is 40 degrees greater than that of the smallest angle"
+a%5B2%5D=a%5B3%5D%2B40+ [3]

substituting for +a%5B3%5D+ in [1] using [2] and [3] gives
+3a%5B3%5D+%2B+%28a%5B3%5D+%2B+40%29+%2Ba%5B3%5D+=+180+=+5a%5B3%5D+%2B+40+
hence
+5a%5B3%5D+=+%28180-40%29+
or


Using [3] gives
+a2+=+a%5B3%5D%2B40+=+28+%2B+40+=+68+

Checking in [1]
a[1], a[2], a[3] = 84 + 68 + 28 = 180 QED
The 3 angles are 28, 68 and 84 degrees.