According to the boron trichloride (BCl3) entry on WebElements, the shape of BCl3 is trigonal planar, which means that the bond angles are all 120 degrees. Boron forms the same types of bonds with chlorine as it does with the other halogens, so boron trichloride has the same molecule structure and bond angles as other boron fluoride.
The best method for determining the bond angles of simple molecules is to consider Valence-Shell Electron-Pair Repulsion Theory (VSEPR). This theory is based on the electrical repulsion of like charges and assumes that the lowest energy state for a molecule spreads out the electron pairs so that there is minimal repulsion between electron pairs. BCl3 has three electron pairs on the central atom (boron), so the shape that minimizes repulsion between these electron pairs is an equilateral triangle.
In order to use VSEPR to determine the bond angles of other molecules, it's important to first draw the Lewis structure of the molecule. To draw the Lewis structure, one must determine how many valence electrons the atoms have, then draw these electrons as dots around the outside of the molecule. In the case of boron, there would be three single electrons, and for chlorine, there would be three electron pairs and one single electron. From the Lewis structure of BCl3, it is clear that there are three electron pairs formed between the boron atom and each of the three chlorine atoms. Once it is determined how many electron pairs there are around the central atom, the rest of VSEPR can be applied.