PAT Breakdown #3: All about angle ranking

What to expect

On the the Dental Admission Test (DAT), you will have a total of 15 angle ranking questions (#31–45 of the PAT section). You will see four angles, which may be obtuse, acute, or right angles. These angles may appear similar at first glance, but the measure of their interior angles will vary by a few degrees. Your goal is to rank the interior angles, from smallest to largest. Here’s an example of an angle ranking question you might see on the DAT:

The rules

The rules for this section are simple:

  • The angles can be rotated any which way, and their side lengths may vary. The angles might be scaled differently, too. Don’t let this confuse you — you only need to focus on the measure of the interior angles.

The strategies

  • Practice makes perfect. It’s true for every PAT question type! With time and practice, you will be able to discern increasingly small differences in the interior angle measurements. Do practice sets, use the angle ranking generator on, and download the CrackDAT app to practice in your spare time. You will improve your speed and accuracy as you familiarize yourself with angle ranking, so set aside at least 10–15 minutes each day to practice and learn from your mistakes, and don’t give up!
  • Use a visualization technique. The goal of these techniques is to visualize the angles in a way that allows you to more easily discern their differences. Here are some techniques — see if any of them work for you. Also note that you don’t need to use the same technique each time. No technique is foolproof or guaranteed to help with every question, but with an arsenal of 2–4 techniques that work for you, you’re more likely to be able to figure out the correct answer.

Laptop method

The “laptop” on the left is more open than the “laptop” on the right. The anterior angle on the left is larger.

Paper cup method

The “cup” on the left would clearly hold a larger volume of water than the one on the right. Therefore, the angle on the left larger and has a larger interior angle than the one on the right.

Angle fitting method

Knife/sharp objects method

Hill method

For (almost) right angles

Imagine that you need to discern which blue angle is larger. Because both angles are relatively close to being right (90-degree) angles, you can compare both to perfect 90-degree right angles. Mentally draw in the dashed line shown, then see which is closer to being a perfect right angle. In the image above, the blue angle on the right is closer. Therefore, it must have a larger interior angle measurement than the blue angle on the left.

For very obtuse angles

In a similar way, you can compare obtuse angles to 180-degree straight lines. Take the example below:

A. 1–2–3–4

B. 1–3–2–4

C. 3–1–2–4

D. 3–4–2–1

First, just figure out which angle is the smallest. Based on the answer choices, you’ll only need to compare Angles 1 and 3. Say you deem Angle 3 the smallest angle. Thus, eliminate A and B. Now, all you have to do to choose between answer choices C and D is determine which angle is the largest — Angle 4 or Angle 1. If you can figure that out, you’re done!

A. 1–4–2–3

B. 4–1–2–3

C. 1–2–3–4

D. 3–1–2–4

Imagine that, looking at the angles, you’re having a difficult time determining the ranking. However, you’re certain of one thing: Angle 2 is smaller than Angle 4. That means the correct answer choice MUST rank Angle 2 before Angle 4. Looking at the above answer choices, answers A and B can thus be eliminated, as both rank Angle 4 before Angle 2. By using your answer choices, you narrowed down the options by 50%. Now, even if you have to take your best guess, you have a 50% chance of choosing the correct answer!



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