Phew, finally I got some time to answer properly. First of all, I think you should study '주동', '사동', '능동', and '피동' expressions. Since '사동' is the opposite of '주동' and '피동' is the opposite of '능동', I'll explain only '사동' and '피동' to you.
사동(使動): This is the case when we order someone to do a specific action. Verbs which imply the meaning is called '사동사'.
피동(被動): This is the case when an action is done by someone else. Verbs which imply the meaning is called '피동사'.
So '주동' simply means one doing something oneself, and 능동 is almost the same notion.
Now, let's see the examples you posted:
<넓을 거리(a street that will be wide)> - Everyone knows that a street cannot be wider itself, since a street is neither a living creature nor a automated width-adjusting machine. So, the only way that a street can be widened is to extend(reconstruct) it by hiring workers. So this example can be explained as a '피동' situation.
<굵을 나무(a tree that will be big and thick)> - Actually it is a little bit awkward to claim this as a 피동 situation since one might perceive the situation like: 'The one that makes tree to grow is the tree itself'. So it looks like one should roughly accept as 'If the environment which tree grows in is not sufficient the tree can't grow'. So anyway it also leads to '피동' situation.
And for the last, there are two ways that a verb can transform into 피동사:
1) Adding one of these in the end: '-이-', '-히-', '-리-', '-기-'
2) Adding '-아-' or '-어-' with '-지다' in the end
which means that the second rule should be applied to both of the examples. Hope this helped.