Students will learn what the central angle theorem is, see its proof, and practice using the theorem. After that, have your students draw some 5-pointed stars, then find the sum of interior angles for each. After doing this for a couple stars, they will likely assume the pattern holds for all stars. The next step is to ask your students to prove it. Here are two possible explanations. Here's a third.
Conclude by giving your students these challenges:
- 2019 Math Kangaroo Levels 11-12 Problem #16 by STEM4all
- Card Trick 1 by NRICH
- Amazing Card Trick by NRICH
- Inclusion Exclusion by NRICH
- Eminit by NRICH
- 2018 AMC 8, Problem 15