To find the measure of the smallest angle of the triangle, we need to add up all the angles and then find the smallest one.
So we have:
2x + 96 + x + 12 = 180 (sum of angles in a triangle is 180 degrees)
Combining like terms, we get:
3x + 108 = 180
Subtracting 108 from both sides:
3x = 72
Dividing by 3:
x = 24
Now we can find the measure of the smallest angle by substituting x back into the equation for the smallest angle:
2x = 2(24) = 48 degrees
Therefore, the smallest angle of the triangle measures 48 degrees.