2x + x+12 + 96 degrees
find the smallest angle of the triangle
To find the smallest angle of the triangle, we need to find the smallest value among the angles given.
The equation given is 2x + x+12 + 96 degrees. Combining like terms, we have 3x+12 + 96 degrees.
To find the smallest value of x, we need to minimize the expression 3x+12.
To minimize this expression, we set its derivative equal to zero:
d/dx (3x+12) = 3 = 0.
Since the derivative is a constant, it does not equal zero for any value of x. Therefore, the expression 3x+12 has no minimum value.
However, we can still find the smallest angle of the triangle by plugging in the smallest possible value of x, which is negative infinity.
When x approaches negative infinity, 3x+12 approaches negative infinity. Therefore, the smallest angle of the triangle is negative infinity degrees.
Note: In a real triangle, angles cannot be negative or greater than 180 degrees.