27.已知,直線MN分別交直線AB,CD于點(diǎn)E和F,且∠MEB=∠CFN.
(1)如圖1,求證:AB∥CD.
(2)如圖2,點(diǎn)G在MN上,且在AB,CD之間,點(diǎn)H,Q分別在AB和CD上,則∠AHG,∠HGQ,∠CQG的數(shù)量關(guān)系為
.
(3)在(2)的條件下,如圖3,HP平分∠BHG,QP平分∠DQG,過(guò)點(diǎn)H作HK∥GQ交CD于點(diǎn)K,連接HQ,若HQ平分∠GHK,∠GQP=2∠QHP,求∠BHK的度數(shù).