Angle Ranking aka Angle Discrimination:

Angle Ranking

According to the last report of the ADA, in the angle ranking section, there are four angles that you must rank from smallest to largest interior angle.
You may have already solved a few of these problems and noticed that in many cases it is not easy to tell the difference in degrees between two angles just by looking at them. Some angles are very close in size that it is almost impossible to tell the difference just by having a glance at them. So there are some strategies here to help you get to the correct order of the angles to choose the right answer.
There are many techniques with different names for doing angle ranking, we will explain each one here. You must try them out and see which one works best for you.

Angle Ranking Strategy:

Most of the techniques in angle ranking require you to first look at the answer choices and see what either the smallest or largest angles are before you look at the shapes. Most of the time, there are two choices: the smallest or largest angles. Then you look at the angles and try to find out which one is the smallest or largest. When you decide one angle is the smallest or largest of the ones mentioned in the options, you can eliminate the wrong answer choices and continue with the ones left. At this point usually comparing two other angles will give you the right answer, you should compare two angles just like the first two you compare.

Angle Ranking Practice Test:

For example, you have 1 and 3 as the smallest angle choices and 2 and 4 as the largest in all four options provided. If you find out which one is the smallest between the two you eliminate 2 choices (see Figure below). Then you just have to compare two other angles or the largest angles to find the right answer to the angle ranking question. Although not all of the questions are like this regarding their options, the elimination process is the same.

An example of angle ranking question
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Techniques

  • Comparing Angles
  • Rapid Eye Movement
  • Drawing a Line/Circle Method
  • Looking From a Distance
  • Reference Method
  • Knife Method
  • Laptop Method
  • Hill Method

Let’s dive into each and review the examples. 

Comparing Angles Technique:

 You can use this method in conjunction with other methods in the angle ranking section of the PAT. First, go to the answer choices and find comparisons between the smallest and largest answers provided. The smallest is naturally the first number in each option and the largest is the last number. Have a look at the angle ranking examples to better understand this point. You should find answer choices that have only two different angle choices in either the largest or smallest angle answers.

Comparing Angles method in a Practice Test:

It is best to compare the smallest and largest angle answer choices. Since they will provide you with either the correct smallest or the correct biggest angle choice. Don’t start angle ranking questions by comparing intermediate angles, it can be confusing and misleading. It can be done when you have decided on the smallest and/or the largest angle.
After locating a comparison between two angles, eliminate the options that do not have that ranking. This can be done just before you even look at other angles to start comparing them. For example, if you first find the smallest angle, eliminate the choices that do not have that ranking order. And then start comparing other angles.
Usually, if you find the smallest angle (or the largest angle), you should try to find the largest angle (or the smallest angle). Whenever you succeed in finding both, the final answer would be clear. So you don’t even have to match up intermediate angles.

Here is an example of using this technique in a real angle ranking problem:

Comparing Angles Technique questions
answer choices in angle ranking questions

So here we have 3 choices for the smallest angle, 1, 3, and 4. So instead of matching up the smallest angles, which are three here, we can compare the largest angles. There are only two options available as the largest angle, which are 2 and 4. When you have done that and have concluded that angle 4 is the largest. Thus, you can eliminate choices A and C. Now to determine the right answer, we go to the smallest angles which are 1 and 3. When you find out number 3 is the smallest angle, you have to find the final answer which is B. So there was no need to compare the intermediate angles.

answer choices in comparing angle ranking dat

Rapid Eye Movement Technique:

In this technique, you try to compare the two angles by looking at them rapidly and figuring out which is smaller or larger. For example, you look at number three and after 1 or 2 seconds look at number four. Then you repeat this until you can see which is smaller.
The shapes are drawn in a way that is not easy to find out which is smaller. A line is much shorter in one shape and in another shape both lines are identical. On the other hand, one shape has the angle facing upward while the other one is facing sideways. You can just focus on the vertex or you can focus on the angle as a whole. If one line is shorter than the other one that makes it look smaller.

Rapid Eye Movement method in a Practice Test:

example of rapid eye movement technique

For example, look at the following angles of an angle ranking question:

At first glance, it is not easy to say which one is larger. But you can cover both lines of the two shapes with your hands for example so that you can see them in a way that they look alike. Then it becomes easier for you to see which one is smaller. You can also just try to look back and forth at the two shapes so quickly. It becomes easy for you to see which is smaller [which is a common method in angle ranking problems].
You can do this by either just looking at the vertexes of the two shapes. Additionally, you can look at the angles in their entirety to see which one is smaller, then choose whichever works best for you.
Another tip that is going to be helpful, especially in comparing small angles is that the one that looks more black, is smaller. This means if the two lines that make the angle are closer to each other, the black color is more visible in the smaller angle than the larger one.

Drawing a Line Technique (or Circle Method):

 Concentrate on the interior areas of the two similar angles and mentally draw a circle around the innermost areas of the angles, or draw a line to make a perfect triangle, whichever you prefer. Use the rapid eye movement technique between the two shapes to find out which angle is smaller. In angle ranking questions we need to be fast. So I personally prefer drawing a line since it is less effort and less distracting. Overall this method is more straightforward than drawing a circle.

example of drawing a line technique

Looking from a Distance Technique:

 According to many people, looking from a distance helps you see the difference between two angles better. However, many people can see better from up close. So again you must find out which one works best for you.

Reference Technique:

In this technique, we use 90 and 180 degrees as our reference. Here you must visualize or draw a third line that will make the angle either a straight line or a right angle. In the first example of an angle ranking question below, the angles on the left are acute angles, therefore, they can be referenced to 90 degrees (purple lines). The angle closest to 90 degrees is the bigger angle, which is option one here.
In the second example of a real angle ranking problem, the two angles are closer to a straight line than a right angle. That is to say, they are obtuse angles, so they must be referenced to 180 degrees. Therefore, the angle closer to being a straight line is the larger angle, which is option two. This technique is most helpful when the angles in angle ranking questions are between 60-120 and 150-210. Notice that when you draw a purple line, the line that is closer to this line has a larger interior angle.

the first example of reference technique
the second example of reference technique

Knife Technique:

This technique requires you to see the angle as the tip of a knife in angle ranking problems. This technique focuses on the intersection of the lines rather than the angle itself. You should find the tip of the knife that is thinner and sharper. Hence, it will cut deeper. Here is another real angle ranking question:

example of knife technique

Laptop Technique:

Imagine the angles in angle ranking questions are laptops and the one that is the closest to being closed is the smallest. So the laptop that is furthest from being closed is the largest.

example of laptop technique

Hill Technique:

This technique involves imagining a rider standing on one side of the angles, then trying to ride down. For obtuse angles, if the interior angle is near 90 degrees (alpha1 in the Figure) then the intersection of two lines is NOT safe. As long as the angle tends to 180 degrees (alpha3 in the Figure) the rider is able to ride down safely.

 For acute angles, the safest path is the smallest angle which is near zero (beta3 in the Figure). Whenever the interior angle tends to 90 degrees (beta1 in the Figure), the intersection of two lines is not safe for the rider so the rider cannot be fast. Therefore, if the angles are less than 90 degrees, the one that makes you ride faster down the hill is the smaller angle. And if the angles are more than 90 degrees then the one that makes you ride faster will be the larger.

example of hill technique

Conclusion

Overall, there are many techniques that are essentially the same but have different names, in these methods you need to use your visualization or imagination to get the right answer. In different methods you should look at the angles like they are laptops being closed, or like they are hills and people are standing on the slope, or they are knives and you should decide which has a sharper tip, or mountains, or slices of cake and decide which is smaller, or try parking the angles inside each other to see which is smaller and so on. What all these techniques have in common is that you should try to imagine and visualize in whichever way suits you to try to see which angle is smaller. Remember you have around 30 seconds to solve each angle ranking problem, but through practice, you can solve them much faster and more accurately.

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