Angles in polygons

There are 71 NRICH Mathematical resources connected to Angles in polygons
Isosceles Seven
problem
Favourite

Isosceles seven

Age
14 to 16
Challenge level
filled star empty star empty star

Is it possible to find the angles in this rather special isosceles triangle?

Triangle or No Triangle?
problem
Favourite

Triangle or no triangle?

Age
5 to 7
Challenge level
filled star empty star empty star

Here is a selection of different shapes. Can you work out which ones are triangles, and why?

Name That Triangle!
problem
Favourite

Name that triangle!

Age
7 to 11
Challenge level
filled star empty star empty star

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?

Polygon Rings
problem
Favourite

Polygon rings

Age
11 to 14
Challenge level
filled star empty star empty star

Join pentagons together edge to edge. Will they form a ring?

Walking round a triangle
problem
Favourite

Walking round a triangle

Age
5 to 7
Challenge level
filled star empty star empty star
This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?
Round a hexagon
problem
Favourite

Round a hexagon

Age
7 to 11
Challenge level
filled star empty star empty star

This problem shows that the external angles of an irregular hexagon add to a circle.

Cyclic Quadrilaterals
problem
Favourite

Cyclic quadrilaterals

Age
11 to 16
Challenge level
filled star empty star empty star

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

Triangles and petals
problem
Favourite

Triangles and petals

Age
14 to 16
Challenge level
filled star filled star empty star
An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?
Semi-regular Tessellations
problem
Favourite

Semi-regular tessellations

Age
11 to 16
Challenge level
filled star empty star empty star

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Which solids can we make?
problem
Favourite

Which solids can we make?

Age
11 to 14
Challenge level
filled star filled star filled star

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?