Math PicnicFree printable practice

Angles in a polygon worksheets

Every polygon's angles add to a number you can work out rather than look up. These free printable worksheets ask for the total for a shape with a given number of sides, and sometimes for the size of a single angle in a regular one.

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Angles in a polygon
Angles in a polygon worksheet — Three to eight sides, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

The rule comes from triangles. Any polygon can be cut into triangles from one corner — a pentagon gives three, a hexagon gives four — and each triangle contributes 180°. That is where (n − 2) × 180 comes from, and a child who has drawn the cuts once can rebuild the formula whenever they need it rather than remembering it wrong.

Why this sheet works

The second question is a division and a trap in equal measure. One angle of a regular hexagon is 720 ÷ 6 = 120°, and the division only works because the shape is regular. Both kinds of question appear on the page so a child has to read which is being asked rather than apply the same move eight times.

How this one works

One question from this sheet, worked through a step at a time.

Angles in a hexagon

hexagon6 sides
6−2=4 triangles
4×180=720°
720°
  1. There is no separate rule for each shape. Pick one corner of the hexagon and draw a line from it to every corner it is not already joined to — the whole shape falls into triangles, and you already know what a triangle's angles come to.
  2. Counting them: the corner you started from reaches every other corner except its own two neighbors, so a 6-sided shape splits into 6 − 2 = 4 triangles.
  3. Every triangle's angles add to 180°, and between them the triangles use up every angle of the shape and nothing else. So the whole lot comes to 4 × 180 = 720°.
  4. So the angles of a hexagon add up to 720°.

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