Floored

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?

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).

Getting an Angle

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

Stellar Angles

Stage: 3 Short Challenge Level:
The four marked angles are the interior angles of a quadrilateral. Hence $x=360-(105+115+125)=15$

This problem is taken from the UKMT Mathematical Challenges.