Polygons
Reason about interior angles, exterior turns and diagonals. Explore what regularity allows you to conclude.
Regular and flexible shapes
1 comparison · No time limit · Explore after checking
Example
Example
Compare the angles using only the givens.
Review the comparison
The polygon is regular, with 5 to 12 sides.
Compare one interior angle with its adjacent exterior turn.
One allowed polygon is shown. The drawing does not fix its number of sides.
One interior angle
One exterior turn
Choose an answer to try the example.
Why?
Explore the relationship
Make the interior angle twice the exterior turn.
In this drawing
Need a clue?
The two angles add to 180°. Split that total in the ratio 2 : 1.
Example positions
Add sides. Watch the interior angle grow as the exterior turn shrinks.
The controls preserve the givens. Examples illustrate the rule; the explanation proves it.
Go further Apply the idea
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Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is usedHelp
Choose whether Quantity A is greater, Quantity B is greater, the quantities are equal, or the relationship cannot be determined. Use only the stated givens. A drawing shows one possible case.
Your first checked answer counts. A shown answer counts as 0 correct. A checked comparison is saved immediately, so you can explore afterward without losing your result. An unfinished comparison is not saved as a result.
After checking, use the controls to solve an exploration goal. When the relationship cannot be determined, save two valid cases with different comparisons. Open Go further to apply the idea to a new question. These activities are optional and do not change your score.
Angles and trigonometric functions use degrees. Levels increase the mathematical complexity; they do not measure IQ.
About this practice
Learn a method
Sum polygon anglesReason about interior angles, exterior turns and diagonals. Explore what regularity allows you to conclude.
For a broader mix of practices, explore the geometry practice test. Membership is required to start a test.
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Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is used