# Illuminati triangles

**Geometry**Level 4

- 1 - In the illuminati triangle above, let's name each corner with one letters (A, B or C).
- 2 - Now name the middles of the segments of AB, BC, and CA with a letter (D, E or F).

If you join with a segment all the DE, EF, and FD parts, there should be 4 triangles which the angles are 60º each one. If you repeat the step 2 three times on each triangle, but changing the AB, BC, CA for the news names (eg. DE, EF, FD), there'll be X numbers of 60º angles. If you make this division: \(\frac{X}{N}\) where N is the number of triangles, it'll give you a number of degrees (K).

With Kº, how many scalene triangles can you make?

**BONUS:** and how many isosceles triangles?