Brainlag PlusInterior angle sums, interior and exterior angles of regular polygons, and working back to the number of sides.
Two facts for every polygon
- Interior angles of an n-sided polygon add up to (n − 2) × 180° (it splits into n − 2 triangles).
- Exterior angles of any polygon add up to 360°.
For a regular polygon: exterior angle = 360 ÷ n, and interior angle = 180 − exterior.
- regular octagon: exterior 360 ÷ 8 = 45°
- interior 180 − 45 = 135°
- interior angle 150°: exterior 30°, so 360 ÷ 30 = 12 sides
The rest of this lesson and its 7 practice questions are in Plus.
Screen 1 of 2, free to read.
- 7 exam-style questions, marked as you go, each with a worked solution
- The Scientific Calculator beside every question
- Anything you get wrong is saved to your flashcards