题目

There was a story many years ago of a school teacher—Mrs.  Thompson. She told the children  on the first day that she loved them all the same. But that was a  lie. There in the front row was a little boy named Teddy Stoddard. He didn‘t play well with the other children and he always needed a bath. She did not like him.     Then Mrs. Thompson got to know that Teddy was actually a very good boy before the death of his mother. Mrs. Thompson was ashamed of herself. She felt even worse when, like all her other students, Teddy brought her a Christmas present too. It was his mother’s pe12．平面内的两条直线有相交和平行两种位置关系（1）已知AB平行于CD，如a图，当点P在AB、CD外部时，∠BPD+∠D=∠B即∠BPD=∠B-∠D，为什么？请说明理由．如b图，将点P移动到AB、CD内部，以上结论是否仍然成立？若不成立，则∠BPD、∠B、∠D之间有何数量关系？请说明结论；（2）在图b中，将直线AB绕点B逆时针方向旋转一定角度交直线CD于点Q，如图c，则∠BPD、∠B、∠D、∠BQD之间有何数量关系？（不需证明）（3）根据（2）的结论求图d中∠A+∠B+∠C+∠D+∠E+∠F的度数．