Polygon Angles Worksheet
Goal: Find the interior, exterior and total angles of regular polygons, discover the formulas behind them, and use them to explain which shapes tile a floor.
What to do
- Open the regular polygon explorer and keep “Side length” at 4.
- Press the “3 sides” button and record the interior angle, exterior angle, angle sum and number of diagonals.
- Repeat with the “4 sides”, “5 sides”, “6 sides”, “8 sides” and “12 sides” buttons.
- Type 20 into “Number of sides” and record the last row.
Record your results
| Setting | Interior angle | Exterior angle | Angle sum | Diagonals |
|---|---|---|---|---|
| 3 sides | ||||
| 4 sides | ||||
| 5 sides | ||||
| 6 sides | ||||
| 8 sides | ||||
| 12 sides | ||||
| 20 sides |
Questions
By how much does the angle sum grow each time you add one side? Write a formula for the angle sum of an n-sided polygon.
Multiply each polygon’s exterior angle by its number of sides. What do you notice?
Find the interior angle of a regular octagon by hand.
Which regular polygons in your table can tile a floor with no gaps or overlaps? Use the interior angles to explain.
Use the diagonal formula n(n − 3) ÷ 2 to check your table for 12 and 20 sides.
Challenge: a regular polygon has interior angles of 150°. How many sides does it have?
Free from Geometry Lab · geometrylab.net
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