If I want to calculate a 3D-integral that contains the product of two vectors I can write $\int f(\vec{x}) e^{-i\vec{k}\cdot\vec{x}}\mathrm{d}^3 x = \int f(\vec{x})e^{-ikr\cos{\theta}} r^2\sin{\theta}\:\mathrm{d}r\:\mathrm{d}\theta\:\mathrm{d}\phi $
From wikipedia I know the higher dimensional volume element $r^{n-1}\sin^{n-2}{\phi_1}\sin^{n-3}\phi_2\dots\sin\phi_{n-2}\:\mathrm{d}r\:\mathrm{d}\phi_1\dots$
Which of these angles does the the theta in the first integral correspond to and why?