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.

2. Originally Posted by stellina_91
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.

3. But wouldn't a = 128

As the sum of a quadrilateral is 360 and 52 x 2 = 104

360 - 104 = 256

256/2 = 128

4. Originally Posted by stellina_91
But wouldn't a = 128

As the sum of a quadrilateral is 360 and 52 x 2 = 104

360 - 104 = 256

256/2 = 128
Haha, I'm sorry that I suck. It's 2:30 in the morning here; I'm a little off

I will edit original post, with what I meant.

5. Haha, no worries! I appreciate the help you have given me so far anyway.

6. Originally Posted by stellina_91
Haha, no worries! I appreciate the help you have given me so far anyway.
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.