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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.

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Polygon Cradle

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?

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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: Challenge Level:2 Challenge Level:2
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.