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.

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.