Interior and exterior angle sums of a polygon
- One cut, two triangles — 3 tasks
- The fan from one vertex — 3 tasks
- Count the triangles, not the sides — 3 tasks
- Walk round the outside — 3 tasks
- Going Deeper — 6 tasks
- Practice — 26 tasks
- Summary — 2 tasks
- One idea and one calculation — 3 tasks
Classroom activities
Things a class does rather than writes on. Each one is a finished PDF: print it, cut it up if it says so, and hand it round.
-
Does the Total Grow, or Stay at 360°? — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 polygons with arcs marked at their corners and no numbers. Students do not work anything out: they decide whether the marked angles add up to (n − 2) × 180°, to 360°, or to neither. The exterior angles of a triangle, a pentagon, a hexagon and an octagon all go in the 360° row. The last row holds the mistakes that matter: the angle all the way around the outside, two exterior angles at one corner, and a corner left out.
-
Inside or Outside, Triangles or Sides? Polygon Angles — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a short question about one polygon: a total of interior angles, one interior or exterior angle of a regular polygon, the number of sides, or a missing angle. The wrong answers are the two costliest mistakes on this topic: mixing up the interior and the exterior angle, and counting one triangle for every side. The row of box numbers at the foot is the check.
-
Is That Really an Exterior Angle? — Mystery Picture 25–35 minutes · 4 sheets
25 squares, each a convex polygon with one angle marked at one corner: fill the square if the marked angle is an exterior angle, leave it white if it is not. The white squares are the mistakes students really make: the angle all the way around the outside, the angle between two sides carried on, the interior angle, and a line that does not carry a side straight on. When every square is right, a picture appears.
-
A Total, or Just One Angle? Polygon Angles — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, four kinds mixed together: the total of a polygon's interior angles, the number of sides from that total, one interior angle of a regular polygon, and one exterior angle. Counting a triangle for every side, or giving the interior angle when the exterior one is asked (and the reverse), lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.