There is a simple methodical process in solving angle problems.
Find the largest or smallest angle. In this case it is easy to say that 4 is the largest angle.
You can rule out any of the answer choices that do not have 4 as the largest angle. This leaves you with typically 3 or 4 choices.
Then you find the other angle that is opposite of what you determined in the first step (smallest or largest angle). Rule out any of the remaining choices that do not have the smallest angle as the first angle. This leaves you with typically with 2 choices.
To help determine between the remaining choices, you can try imagining putting one angle into the other angle. For example, you can see that 2 can fit into 3, but 3 cannot fit into 2, so 2 is smaller than 3.
Another way is to put an imaginary line in the angle that would make 90 degrees with one of the lines. The remaining angle (the angle in the answer choices - the angle from the 90 degrees) would leave you with a much smaller angle to compare to each of the other angles in the answer choices. For example, if you imagined a 90 degree angle in 1 and 3, the remaining angle (Angles 1* and 3*) from subtracting the 90 degrees would be smaller in 1 than in 3. Refer to picture for help.
For this particular problem I would recommend comparing each angle to a perfect right angle in your mind. This should lead you to realize that angle 4 is the largest. Many of the angle ranking answers on the actual DAT can be eliminated by simply knowing that angle 4 is the largest. Then you may be only left with 1 or 2 answers that can be correct, and you have a lot greater chance of picking the right answer. I also found it useful to focus on just two angles at a time. Stare at the very base of the angle and shift your eyes back and forth as quickly as you can between the vertices of the two angles you are comparing, for some reason one angle will just appear larger to your eyes, and it is usually right. I would also recommend using something like Crack DAT PAT to prepare yourself on angles. The benefit of a program like that is the angles are much harder than the real thing. I found that the angles on Crack DAT PAT varied from each other by about 2 to 3 degrees, whereas those on the real DAT I would guess varied by about 4 to 5 degrees. If you can train yourself to recognize 2 or 3 degrees, then 4 or 5 degrees will seem like a breeze. The key to success is repetition, repetition, repetition.