Well, to find the bond angle & shape of a compound, you need to first check the hybridization of the central atom. There is a fixed bond angle for a hybridisation(if there are not any lone pairs on the central atom). For example, in CH4, the hybridization of C is sp3, and the bond angle is 109 degrees 28 minutes & the shape is tetrahedral.
But you will also need to check if there are any lone pairs of electrons on the central atom. If there are, then the bond angle will decrease due to lp-bp and/or lp-lp interaction. Also, the shape can change (say, from tetrahedral to V-shape etc.).