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.