  We derive the Weil-Petersson measure on the moduli space of hyperbolic
surfaces with defects of arbitrary opening angles and use this to compute its
volume. We conjecture a matrix integral computing the corresponding volumes and
confirm agreement in simple cases. We combine this mathematical result with the
equivariant localization approach to Jackiw-Teitelboim gravity to justify a
proposed exact solution of pure 2d dilaton gravity for a large class of dilaton
potentials.
