Question 758127: twice the first angle is 20 deg less than the third, 1/2 of the third is 60 deg less than the sum of the 1st and 2nd angles.find the angles
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Three angles, A,B,C;
Just write an equation for what it says.
:
twice the first angle is 20 deg less than the third,
2A = C-20
or
C = 2A+20
:
1/2 of the third is 60 deg less than the sum of the 1st and 2nd angles.
.5C = A + B - 60
multiply both sides by 2
C = 2A + 2B - 120
therefore
2A+20 = A + B - 60
2A - A = B - 60 - 20
A = B-80
or
B = A+80
:
And assuming this is a triangle
A + B + C = 180
replace B with (A+80); replace C with (2A+20)
A + A+80) + 2a+20 = 180
4A + 100 = 180
4A = 180 - 100
4A = 80
Divide both sides by 4
A = 20 degrees
then
B = 20 + 80
B = 100 degrees
and
C = 2(20)+20
C = 60 degrees
:
20 + 100 + 60 = 180; confirms our solutions
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