1. (2021七上·龙凤期末) 如图，ABCD，∠BMN与∠DNM的平分线相交于点G，

完成下面的证明：

∵MG平分∠BMN，

∴∠GMN＝∠BMN（                                    ▲                                           ），

同理∠GNM＝∠DNM．

∵ABCD

∴∠BMN＋∠DNM＝                  ▲                        （                  ▲                        ）．

∴∠GMN＋∠GNM＝                  ▲                         ．

∵∠GMN＋∠GNM＋∠G＝                  ▲                         ，

∴∠G＝                  ▲                         ．