### Bow Tie

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

Weekly Problem 18 - 2007
A regular pentagon together with three sides of a regular hexagon form a cradle. What is the size of one of the angles?

### Hexapentagon

Weekly Problem 53 - 2007
The diagram shows a regular pentagon and regular hexagon which overlap. What is the value of x?

# U in a Pentagon

##### Stage: 3 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

The diagram shows a regular pentagon $PQRST$. The lines $QS$ and $RT$ meet at $U$. What is the size of angle $PUR$?

If you liked this question, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.