### 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?

### Getting an Angle

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

### Convex Polygons

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

# Parallelogram in the Middle

##### Age 11 to 14 Short Challenge Level:

The diagram, which is not drawn accurately, shows a parallelogram inside a triangle.The marked lengths are equal.

What is the value of $x$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.