Angles in polygons

problem

Parallelogram in the Middle

Age

11 to 14

Challenge level

Weekly Problem 27 - 2013
The diagram shows a parallelogram inside a triangle. What is the value of $x$?
problem

Equal Lengths

Age

11 to 14

Challenge level

Weekly Problem 29 - 2013
An equilateral triangle is drawn inside a rhombus, both with equal side lengths. What is one of the angles of the rhombus?
problem

Tessellating Hexagons

Age

11 to 14

Challenge level

Which hexagons tessellate?
problem

Trapezium Arch

Age

11 to 14

Challenge level

Weekly Problem 27 - 2007
Ten stones form an arch. What is the size of the smallest angles of the trapezoidal stones?
problem
Favourite

Walking Round a Triangle

Age

5 to 7

Challenge level

This ladybird is taking a walk round a triangle. Can you see how much she has turned when she gets back to where she started?
problem
Favourite

Triangle or No Triangle?

Age

5 to 7

Challenge level

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

Always, Sometimes or Never? Shape

Age

7 to 11

Challenge level

Are these statements always true, sometimes true or never true?
problem
Favourite

Transformations on a Pegboard

Age

7 to 11

Challenge level

How would you move the bands on the pegboard to alter these shapes?
problem
Favourite

Round a Hexagon

Age

7 to 11

Challenge level

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

Three Triangles

Age

7 to 11

Challenge level

What do you notice when you put three triangles together?