Find the angles a and b in the diagram, GIVING REASONS!
I am not sure how you would figure this out or what the reasons would be.
Thanks.
Since you have a parallelogram, there are a couple of geometric theorems you can use.
angle $\displaystyle b=52$ degrees and $\displaystyle =180-52=128$ degrees
You can find b because it is opposite the given 52 degree angle. Since on this parallelogram, there are 2 equal parallel segments that are intersected by 2 parallel lines, you know these "opposite" angles must be equal.
To find a, you just need to know that if 1 line is intersected by 2 parallel lines, the 2 angles must total to be 180 degrees.
Edit...Sorry, I did complimentary when I meant to do supplementary.
The same reasoning applies though.
The way you did it is another way to do it, if you feel more comfortable using the total internal angles being 360, but I find my way to be a little easier, because it's just simple addition, and you don't have to do any division. Plus, I think it's easier to see supplementary angles than it is to visualize an entire parallelogram. Either way works just the same, and should get you the same answer though.