Angle Discrimination (Angle Ranking):
In angle ranking, 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 from smallest to biggest and 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.
Most of these techniques 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 as either the smallest or largest angles. Then you go on and 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 to angles just like the first two you compare.
For example when 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 question. Although not all of the questions are like this regarding their options, the elimination process is the same.
Comparing Angles Technique: You can use this technique in conjunction with other techniques. First, go to the answer choices and find comparisons between the smallest and largest answers provided. The smallest is naturally the first numbers in each option and the largest are the last numbers, have a look at the 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.
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 by comparing intermediate angles, it can be confusing and misleading, do it after you have decided the smallest and/or the largest angle.
After locating a comparison between two angles, eliminate answer choices that do not have that ranking before you even look at other angles to start comparing them. For example, if you find the smallest angle, eliminate the choices that do not have that ranking order first 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), and if you succeed in finding both, you often find the final answer and don’t even have to compare intermediate angles.
Here is an example of this technique:
So here we have 3 choices for the smallest angle, 1, 3, and 4. So instead of comparing the smallest angles, which are three here, we can compare the largest angles since 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, you can eliminate choices A and C. Now to determine the right answer, we go to the smallest angle answer choices 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.
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, and 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 like one line is much shorter in one shape and in the other shape both lines are identical, or 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 which makes it look smaller.
For example, look at the following angles
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 that it becomes easy for you to see which is smaller.
You can do this by either just looking at the vertexes of the two shapes or looking at the angles in their entirety to see which one is smaller, 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 going to be 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. I personally prefer drawing a line since it is less effort and less distracting and overall more straightforward than drawing a circle.
Looking from a Distance Technique: According to many people, looking from a distance helps you see the difference between two angles better, but 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 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, 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 question 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.
Knife Technique: This technique requires you to see the angle as the tip of a knife. 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.
Laptop Technique: Imagine the angles in 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.
Hill Technique: This technique involves imagining two people each standing on one of the slopes at both angles. The rules for this technique is if the angles are less than 90 degrees, the one that makes you run faster down the hill is the larger. And if the angles are more than 90 degrees then the one that makes you run faster will be the smaller.
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 that 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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