You may also like

problem icon


A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?

problem icon

Pie Cuts

Investigate the different ways of cutting a perfectly circular pie into equal pieces using exactly 3 cuts. The cuts have to be along chords of the circle (which might be diameters).

problem icon

Getting an Angle

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

Right Angled Octagon

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

$6$ right angles can be achieved, as in the diagram below:


If there were seven right angles, these would be a total of $7 \times 90^\circ = 630^\circ$. The total interior angle of an octagon is $6 \times 180^\circ = 1080^\circ$, so the final angle would have to be $1080^\circ - 630^\circ = 450^\circ$. The interior angle cannot be more than $360^\circ$, so this cannot be achieved.

This problem is taken from the UKMT Mathematical Challenges.