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2007-10-20 05:20:58 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
x = 5.
How to get it:
This is a pair of simultaneous eqts.
Eqt1: 2x+40 + 4x^2 + 6x = 180 (angle sum of triangle)
Eqt2: 2x+40 + 4x^2 = 6x^2 (ext. angle of triangle)
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Eqt2====>2x+40 - 2x^2 = 0
Eqt1 - Eqt2
6x^2 + 6x = 180
x^2 + x - 30 = 0
(x + 6)(x - 5) = 0
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'.' the choices (4, 5, 7, 10) have no negative answer
.'. x = 5.
2007-10-20 05:27:01 · answer #1 · answered by Adrienne 6 · 0⤊ 0⤋
5
2007-10-20 05:27:49 · answer #2 · answered by john 4 · 1⤊ 1⤋
x = 5
2007-10-20 05:25:56 · answer #3 · answered by azman salleh 1 · 1⤊ 0⤋
There are 2 ways to solve this
Either solve : 6x^2 +6x =180
6x^2 +6x -180 =0
or solve the other equation: 4x^2 +6x +2x +40 =180
4x^2 +8x -140 =0
let's solve this last equation
4x^2 +8x -140 =0
dividing by 4 we get
x^2 +2x -35 =0
Discriminant = 4 +4(35) = 144 = (12)^2
x1 = (-2 +12)/2 = 5
x2 = (-2-12)/2 =-7
this is not allowed
hence x =5 is the solution.
2007-10-20 05:32:18 · answer #4 · answered by Any day 6 · 1⤊ 0⤋
Answer is 5 - because 6x + 6x^2 = 180
6 x 5 =30
6 x 5 x 5 = 150
30 + 150 = 180
This doesn't work for any of the other values of x.
Drew
2007-10-20 05:28:14 · answer #5 · answered by Andrew W 6 · 0⤊ 0⤋
angles on a straight line are 180 degrees
6x + 6x^2 = 180
6(x+x^2)= 180
x+x^2= 30
5+5^2=30
x=5
Note ^2 means to the power of 2
2007-10-20 05:28:00 · answer #6 · answered by Anonymous · 1⤊ 0⤋
6x+6x^2=180
x^2+x-30=0 x=((-1+sqrt(1+120))/2= 5 degrees
2007-10-20 05:29:15 · answer #7 · answered by santmann2002 7 · 1⤊ 0⤋