Context : Aims : We have investigated the differences in apparent opening angles between the parsec-scale jets of the active galactic nuclei ( AGN ) detected by the Fermi Large Area Telescope ( LAT ) during its first three months of operations and those of non-LAT-detected AGN . Methods : We used 15.4 GHz VLBA observations of sources from the 2 cm VLBA MOJAVE program , a subset of which comprise the statistically complete flux density limited MOJAVE sample . We determined the apparent opening angles by analyzing transverse jet profiles from the data in the image plane and by applying a model fitting technique to the data in the ( u,v ) plane . Both methods provided comparable opening angle estimates . Results : The apparent opening angles of \gamma -ray bright blazars are preferentially larger than those of \gamma -ray weak sources . At the same time , we have found the two groups to have similar intrinsic opening angle distributions , based on a smaller subset of sources . This suggests that the jets in \gamma -ray bright AGN are oriented at preferentially smaller angles to the line of sight resulting in a stronger relativistic beaming . The intrinsic jet opening angle and bulk flow Lorentz factor are found to be inversely proportional , as predicted by standard models of compact relativistic jets . If a gas dynamical jet acceleration model is assumed , the ratio of the initial pressure of the plasma in the core region P _ { 0 } to the external pressure P _ { \mathrm { ext } } lies within the range 1.1 to 34.6 , with a best fit estimate of P _ { 0 } / P _ { \mathrm { ext } } \approx 2 . Conclusions :