if post are spaced 10 feet apart for a straight-line fence of 100 feet, then you would need how many post to hang the fence?

There are 11. Remember, there's a post at the very beginning of the fence, and one at the very end. So it's (fence length / 10) + 1 = (100 / 10) + 1 = 10 + 1 = 11.

They're positioned along the fence at the following distances from the start:

0 ft, 10 ft, 20 ft, ..., 100 ft.

That's probably why the question specified "straight-line fence". If it was in a decagon (10-sided polygon shape, so sort of round-ish), the first post could also serve as the last post, and there could be only 10 posts. But in a straight line, there have to be 11.