M3.5.4 For the adult
Angles in polygons
Do the four angles of any four sided shape add up to the same number?
What this chapter teaches
Diagonals from one corner cut a polygon into triangles, and each triangle has 180°. A polygon with n sides makes n − 2 triangles, so its angle sum is (n − 2) × 180°. Dividing by the number of corners gives each angle of a regular polygon.
Three questions to ask
There is no one right wording. Listen for the idea.
- Why do the four angles of every quadrilateral add to 360°?
- How many triangles does a hexagon make, and what is its angle sum?
- How would you find one angle of a regular octagon?
After the chapter, the learner can
- Show that the angles of a quadrilateral add up to 360°
- Work out the angle sum of any polygon
- Find each angle of a regular hexagon
What they copy into their notebook
A polygon with n sides makes n − 2 triangles. Its angle sum is (n − 2) × 180°. A quadrilateral adds to 360°. Each angle of a regular hexagon is 120°.