SOLUTION: Someone please help! One angle of a triangle exceeds another by 23 degrees. The third is 6 degrees less than the sum of the others. Find the measure of the angles. I would

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Question 71419: Someone please help!
One angle of a triangle exceeds another by 23 degrees. The third is 6 degrees less than the sum of the others. Find the measure of the angles.
I would really appreciate it if someone could help with this problem!
thanks!
Found 2 solutions by ptaylor, ankor@dixie-net.com:
Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
Let x=one of the angles
(x+23)=the other angle
(x+(x+23)-6)=the third angle
Now since this is a triangle, all three angles must add up to 180 degrees. So our equation to solve is:
x+(x+23)+(x+(x+23)-6)=180 get rid of parens
x+x+23+x+x+23-6=180 collect like terms
4x+40=180 subtract 40 from both sides
4x+40-40=180-40 collect like terms again
4x=140 divide both sides by 4
x=35 degrees-------------------one of the angles
(x+23)=35+23=58 degrees-------------the other angle
(x+(x+23)-6)=35+35+23-6=87 degrees------the third angle
CK
87+58+35=180
180=180
also
35+23=58
58=58
and
35+58-6=87
87=87
Hope this helps----ptaylor

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Let x = one angle
:
Write an expression for each statement:
:
"One angle of a triangle exceeds another by 23 degrees."
(x + 23)
"The third is 6 degrees less than the sum of the others."
x + (x+23) - 6
Simplify:
2x + 17
:
Find the measure of the angles.
We know the total of all 3 angles is 180, a simple equation:
:
x + (x+23) + (2x+17) = 180
x + x + 23 + 2x + 17 = 180
4x + 40 = 180
4x = 180 - 40; subtracted 40 from both sides
4x = 140
x = 140/4
x = 35 degrees is the 1st angle
:
2nd angle: (x+23)
35 + 23 = 58 degrees is the 2nd angle
:
3rd angle: 2x + 17
2(35) + 17 = 87 degrees is the 3rd angle
:
:
Check: 35 + 58 + 87 = 180
:
Not that hard, right?