On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?
How good are you at estimating angles?
Explore patterns based on a rhombus. How can you enlarge the
pattern - or explode it?
$ABCD$ is a square. $P$ and $Q$ are points outside the square such that triangles $ABP$ and $BCQ$ are both equilateral. How big is angle $PQB$?
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.View the archive of all weekly problems grouped by curriculum topic