Conclude by giving your students these challenges:

- Penta Colour by NRICH
- Root to Poly by NRICH
- Rainstorm Sudoku by NRICH
- Exact Dilutions by NRICH
- Pencil Prices

Find \(x{:}\)

There are two elegant ways to solve this problem, both of which can be done mentally. Here's the first way: Notice that \(ACEDB\) is a pentagon, and thus, it's interior angles sum to \(540^\circ.\) Notice that \(\angle DEC = 360^\circ - 160^\circ = 200^\circ.\) Adding up the known angles in the pentagon, gives us \(80^\circ + 20^\circ + 200^\circ + 10^\circ = 310^\circ.\) But we need \(540^\circ,\) so the missing angle, \(\angle BDE,\) must be \(230^\circ.\) Thus, \(x = 360^\circ - 230^\circ = 130^\circ.\) Here's the second way: Start by drawing \(\overline{BC}.\) Notice that \(\triangle ABC\) has \(80^\circ + 20^\circ + 10^\circ = 110^\circ,\) so it's lacking \(70^\circ.\) Also, notice that \(BDEC\) is a quadrilateral, and thus, it's interior angles sum to \(360^\circ.\) Adding up the known angles in the quadrilateral, gives us \(160^\circ + 70^\circ = 230^\circ,\) but we need \(360^\circ,\) so \(x = 360^\circ - 230^\circ = 130^\circ.\)