Angles in polygons

problem
No right angle here

Age

14 to 16

Challenge level

Prove that the internal angle bisectors of a triangle will never be perpendicular to each other.
problem
Getting an angle

Age

11 to 14

Challenge level

How can you make an angle of 60 degrees by folding a sheet of paper twice?
problem
Convex polygons

Age

11 to 14

Challenge level

Show that among the interior angles of a convex polygon there cannot be more than three acute angles.
problem
Heptagon has

Age

11 to 14

Challenge level

Weekly Problem 15 - 2012
How many of the five properties can a heptagon have?
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
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
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?