Final answer:
To make line 'f' parallel to line 'g', the value of 'x' must be 8, since it allows the slopes represented by angles 1 and 3 to be equal.
Step-by-step explanation:
To determine the value of 'x' that makes line 'f' parallel to line 'g', we need to establish that their slopes are equal, because parallel lines have the same slope. We are given that the measure of angle 3 (m<3) is 7x + 14 and the measure of angle 1 (m<1) is 8x + 6. If 'f' and 'g' are to be parallel, then angles 1 and 3 must be corresponding angles, and thus, they are equal. This allows us to set the two expressions equal to each other:
7x + 14 = 8x + 6.
Now, let's solve for 'x' by rearranging the equation:
7x - 8x = 6 - 14,
-x = -8,
x = 8.
Thus, the value of 'x' must be 8 for line 'f' to be parallel to line 'g'.