Angles in polygons

problem
Which solids can we make?

Age

11 to 14

Challenge level

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?
problem
Semi-regular tessellations

Age

11 to 16

Challenge level

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

Age

11 to 16

Challenge level

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

Age

14 to 16

Challenge level

Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.
problem
Making sixty

Age

14 to 16

Challenge level

Why does this fold create an angle of sixty degrees?
problem
Isosceles seven

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
problem
Triangles and petals

Age

14 to 16

Challenge level

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?
problem
Angles in three squares

Age

14 to 16

Challenge level

Drawing the right diagram can help you to prove a result about the angles in a line of squares.
problem
Pentakite

Age

14 to 18

Challenge level

Given a regular pentagon, can you find the distance between two non-adjacent vertices?