Problem 18 of 34geo-018
A floor tile is a regular hexagon: it has 6 equal sides and 6 equal angles. What is the sum of the measures of the 6 interior angles of the tile?
Try it first
The walkthrough opens once you check an answer.
Solution walkthrough1:17
- We know one angle fact for sure: the angles of any triangle add to . So cut the hexagon into triangles.
- From one corner, draw a line to every corner it is not already joined to. That makes triangles.
- The angles of the triangles exactly fill the angles of the hexagon, so the sum is .
- Traps: counts triangles, is for a 4-sided shape, and is just one angle.