Question

If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough. True False

Answer 1

Very true.
It is only parallel line that can not meet. If the two lines were parallel, then the sum of the inner angles on one side after meeting the third line would be one right angle or more.

Since this is not the case, taking the two angles to be x and y, then,
x+y<2(90)
x+y<180.

This can only mean that the two line must meet to make the third angle, z.
x+y+z=180. (The sum of angles in a triangle).