The pentagon below has two \(90^\circ\) angles, and three \(120^\circ\) angles. This pentagon happens to tile the plane. Can you find an explanation as to why?

Here's my answer:

Two copies of the pentagon fit together to make a regular hexagon, that's been vertically stretched, ever-so-slightly.

Because the regular hexagon tiles the plane, so must this pentagon.

Conclude by giving your students these challenges:

- One to Eight by NRICH
- How Odd by NRICH
- How Steep Is the Slope? by NRICH
- 2000 AMC 8, Problem 19
- Autobiographical Numbers by Pierce School: Problem / Solution