SOLUTION: The second angle of a triangle is 3 times as large as the first. The third angle is 20 degree more than the sum of the other 2 angles. Find the measure of the third angle.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The second angle of a triangle is 3 times as large as the first. The third angle is 20 degree more than the sum of the other 2 angles. Find the measure of the third angle.      Log On


   

Question 70140: The second angle of a triangle is 3 times as large as the first. The third angle is 20 degree more than the sum of the other 2 angles. Find the measure of the third angle.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Three angles, A, B & C = 180
:
"The second angle of a triangle is 3 times as large as the first."
B = 3A
:
"The third angle is 20 degree more than the sum of the other 2 angles."
C = A + B + 20
:
Substitute 3A for B in the above equation:
C = A + 3A + 20
C = 4A + 20
:
We know all three angels in terms of A
:
A + 3A + + 4A + 20 = 180
8A = 180 - 20
8A = 160
A = 160/8
A = 20 degrees
:
B = 3(20)
B = 60 degree
:
Find the measure of the third:
C = 20 + 60 + 20
C = 100 degrees