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The given two angles of a triangle are x+17 and 3x+28.Therefore the remaining angle ? = 180 - sum of the given two given angles.
Therefore ? = 180 - (x+17+3x+28) = 180 - (4x+45) = 135-4x.
Therefore ? = 135-4x.
Therefore , the exterior angle of (135-4x) = 180 - (135-4x) = 45+4x.
But it is given that this angle is equal to x^2 .
So 4x+45 = x^2.
Or x^2-4x-45 = 0
x^2 -9x+5x - 45 = 0
x(x-9) +5(x-9) = 0
(x-9)(x+5) = 0.
Therefore x = 9.
The first step is to set up 2 equations.
The first is the sum of the interior angles.
The second is the addition of 2 adjacent angles.
x^2 + y = 180
Solve the 2nd equation for y.
Then substitue into equation 1 giving
by combining like terms you get
Subtract 180 from both sides
Multiple both sides by -1 in order to get x^2 term positive
Now use quadratic formula
x=(-(-4) (+/-) sqrt(-4^2-4*1*-45))/(2*1)
[4 (+/-) sqrt(196)]/2
-10/2 = -5 18/2 = 9 answer cannot be negative so x = 9
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