SOLUTION: The second angle of a triangle is three times as large as the first. The third angle is 20 degrees less than the sum of the other two angles. What is the sum of the first angle.

Question 564249: The second angle of a triangle is three times as large as the first. The third angle is 20 degrees less than the sum of the other two angles. What is the sum of the first angle.
Answer by TutorDelphia(193) (Show Source): You can put this solution on YOUR website!
This problem can be solved by making a number of substitutions...replacing variables with things of equal value. To keep everything straight, I named my variables f for first, s for second and t for third.
The second angle of a triangle is three times as large as the first gives us:
s=3f
The third angle is 20 degrees less than the sum of the other two angles gives us
t=f+s-20
but we already know that s=3f so we get
t=f+3f-20
combine like terms
t=4f-20
Now here is the unwritten fact that you just have to know about triangles. The sum of the angles in a triangle add up to 180 which gives us
f+s+t=180
plug in 3f for s
f+3f+t=180
plug in 4f-20 for t
f+3f+4f-20=180
combine like terms
8f-20=180
add 20 to both sides
8f=200
divide by 8
f=25
Now that we know f, s is easy to find:
s=3*25
s=75
Same with t, just plug in 25 for f and 75 for s
t=25+75-20
t=80
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