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Angle Ranking (AR) Questions

What is an angle ranking problem?

Angle ranking problems are the third group of problems that appear on the perceptual ability test (PAT) of the dental admissions test (DAT) and comprise Items 31-45. For each angle problem, you will be shown four different angles, labeled 1, 2, 3, and 4. Your task is to rank the angles from SMALLEST to LARGEST and select the answer with the correct ranking.

3 - Angle ranking 1 1.svg
Here are the rules:

Angles must be viewed by their inner angles - i.e. by the smallest angle formed by the two intersecting “arms” shown.


All angles differ by at least one degree. As such, there is only one correct angle ranking and only one correct answer choice.


Angles can be turned in different directions and shown with different “arm” lengths. Some angles may even have “asymmetrical arms,” with one arm being shorter than the other. None of this should change the way the angle measurement is interpreted.

Note: Directions given on test day may be formatted differently, but objectives are the same.

Example problem

Here is a typical angle ranking problem you’d encounter on your DAT, along with an Erudition-style explanation to help you understand how to solve it.

Group 1352 (1).svg
Suggested solving strategy:

You can start by looking for obvious outliers. It is easiest to see that angle 4 is the largest. Notice that it is closest to a right angle, whereas the other angles look more acute. This allows you to eliminate Choice D.

e - Angles L2 #6_Comparison 1.svg

It may be easiest to compare angles 1 and 3 next, since they are oriented the same way; notice that angle 3 is narrower towards its tip and is therefore the smallest angle. This lets you eliminate Choice B.

e - Angles L2 #6_Comparison 2.svg

You still need to compare angles 1 and 2. Since angle 1 has uneven legs, try looking at an area where they both have legs. And, it might help to turn your head to view each angle from a similar perspective/straight on. This will make it easier to see that angle 2 is more open, and you can eliminate Choice C, and Choice A is correct.

e - Angles L2 #6_Comparison 3.svg

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AR tips & strategies!

Look for obvious outliers first, and eliminate answer choices immediately, based on these.

Frame 1283 (1).svg

For acute angles, make sure you’re focusing on areas that are equidistant from the angles’ tips when you’re comparing angles. You may find it’s easier to focus a little closer towards the tip; or start from the tip and move outwards if if helps you to see which angles are opening faster.

Angles L2 #11 - full problem-03 1.svg

For large acute or near-right angles, try comparing the angles to right angles in your head. Sometimes it can also help to compare angles that are oriented similarly first.

Angles L2 #15 - full problem-05 1.svg

For problems containing angles with uneven legs, compare angles only in the areas where all angles have arms. For instance, for the example below, just look at the regions near the tip where all angles have arms, and focus in this area to compare angles.

Angles L3 #22 - full problem-03 1.svg

For obtuse angles arranged similarly to this, try visualizing them as reclining chairs to more easily see which is more open. You can try to visualize other angles or their arms as objects - like mountain slopes or scissors - if it helps you better perceive differences.

Angles L2 #13 - full problem-03 1.svg

... And more! You’ll find a lot more great angle ranking TIPS and strategies in our course videos and individual problem explanations!

Also check out PAT videos we’ve shared on YouTube!

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