Since you have already turned in the assignment
Here is 2-methyl-2-butene.
If you look at the double bond, only one of those carbons (carbon 3, following the IUPAC numbering, the one on the left in the picture) has a proton. The NMR signal from that proton would be split by protons on the neighboring carbons, carbon 2 (which is the other carbon in the double bond, to the right) and carbon 4. Carbon 2 doesn't have any protons, which means the protons on carbon 3 would be split only by those on carbon 4. Carbon 4 has three identical (by rotation) protons, so the proton on carbon 3 would be split into a quartet (N+1). This would be the "quartet like peak at 5.2 ppm" and one H would be represented by the peak.
I couldn't find a picture of 2-methyl-1-butene that had all the protons, but for the purposes of this example, this picture of 2-methylpropene should be sufficient:
You just have to imagine an extra methyl group on one of the two arms on the right.
If you look at the double bond on this molecule, you will see that carbon 1 (the one on the left) has two protons. They are not quite in identical magnetic environments, because one is cis to an ethyl group and the other trans, but they are so close together that instead of splitting each other, they fall on top of each other and appear to be a singlet (unless you have a really powerful magnet!). They would be split by any protons on adjacent carbons, but there is only one adjacent carbon, carbon 2 which is at the other end of the double bond, and it doesn't have any protons. The protons further out, on the two methyl groups (actually a methyl group and an ethyl group in our vision), are too far away to have an effect. Consequently, all you see is a singlet, but the peak represents two H's. So this would be the "singlet appear[ing] at 4.69 ppm" and would represent two protons.