SOLUTION: in a certain triangle the measure of the second angle is 10 degrees more than three times the first. the third angle measure is equal to the sum of the measures of the other two. f

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Question 566122: in a certain triangle the measure of the second angle is 10 degrees more than three times the first. the third angle measure is equal to the sum of the measures of the other two. find the measures of the three angles.
Answer by TutorDelphia(193) About Me  (Show Source):
You can put this solution on YOUR website!
We have 3 (f for first, s for second, t for third) variables and 3 equations:
the measure of the second angle is 10 degrees more than three times the first.
s=3f+10
the third angle measure is equal to the sum of the measures of the other two:
t=f+s
And we know that interior angles in triangles add up to 180:
f+s+t=180
We can actually sub in for f+s and replace it with t since those are equal values
t+t=180
2t=180
t=90
Now we know that f+s=90
and that s=3f+10
so I can sub in 3f+10 for s
f+3f+10=90
4f+10=90
4f=80
f=20
Which makes the second 70