Q - When is a triangle not a triangle?

A - When it's a pyramid
There are two molecular shapes that could be described as triangular (or trigonal). One is a...errr...a triangle and it is referred to as trigonal planar. The other is effectively a triangular based pyramid, called equally obviously, trigonal pyramidal. The reasons behind the differences in the two are important.

Trigonal planar is flat (i.e planar) so imagine a triangle with three atoms at each corner and one in the middle. Each of the corner atoms are 120degrees apart (i.e. 360/3 = 120). You get trigonal planar when you have three bonded pairs and no lone pairs as that is the furthest the electron pairs can get away from each other. an example is BF3

Trigonal pyramidal is like...erm... a pyramid but a pyramid with a trigonal base (hence the name). The bond angles are 107degrees (no way of working that out you just have to remember). You get trigonal pyramidal when you have 3 bonded pairs and 1 lone pair. The lone pair is more repulsive and pushes the bonded pairs down and  away from being trigonal planar (which is what you would get if the lone pair wasn't there). An example is NH3

P.S. The purple lump on the trigonal pyramidal isn't a comedy hat it is a lone pair of electrons.

Why do you get that 180 bond angle between water molecules?

Right this is difficult to explain without a board pen and some pointing but here we go.  

The 180 degrees I am referring to here is for the H that is covalently bonded to an O on one side and Hydrogen bonded to an O on the other (see picture). 

This hydrogen has a covalent bond on one side (i.e. a bonded pair) and a hydrogen bond on the other. Now, technically the hydrogen bond is not a bonded pair of electrons but the oxygen that the hydrogen is hydrogen bonded to is a big ball of negativity (imagine a fat dementor) that behaves much like having a pair of electrons on that side too. So effectively that hydrogen has 2 bonded pairs, and what shape do molecules with 2 bonded pairs take...straight line. 

So there we go, that is your answer. The actual answer in the exam goes along the lines of...

"...because it has two bonded pairs of electrons and to take the position of minimal repulsion the electron pairs  get as far away from each other as possible which is a straight line."