Well I don't remember any of the actual wordings of the theorems but anyway...

1) mKPM=70

mOPM=120

mO=60

mOKP=70

2) I think this is the Alternate exterior angles theorem

3) I don't remember but you can prove that the angles are congruent and then show the lines to be indeed ||

4) Alternate interior angles or something like that - if lines || and cut by trans. then the angles add up to 180 degrees

5) I would show that both lines have the same slope and are thus ||

If you need the reasons for number one let me know