Final answer:
The range of possible measures of x in a triangle is 2 < x < 12.
Step-by-step explanation:
To find the range of possible measures of x if x-2, 10, and 12 represent measures of the sides of a triangle, we need to understand the triangle inequality theorem. According to this theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. So, in this case, we have:
x + 10 > 12
x + 12 > 10
2 + 10 > x
Solving these inequalities, we can find the range of x:
12 - 10 < x < 2 + 10
2 < x < 12