SOLUTION: A regular hexagon has six vertices with six congruent sides and all six interior angles congruent. If every vertex of the hexagon is connected to every other vertex, find the meau

Algebra ->  Polygons -> SOLUTION: A regular hexagon has six vertices with six congruent sides and all six interior angles congruent. If every vertex of the hexagon is connected to every other vertex, find the meau      Log On


   

Question 173662: A regular hexagon has six vertices with six congruent sides and all six interior angles congruent. If every vertex of the hexagon is connected to every other vertex, find the meausre of the smallest angle formed by any of the connecting lines.
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
30 degrees would be the smallest angle formed by the diagonals of a regular hexagaon. every interior angle is 120 if you take 3 diagonals from any vertex it forms (4) 30 degree angles and there is no other smaller angle formed.
When you take 3 diagonals from any vertex you form 2 trangles on the outside with angles measuring 120,30, and 30 degrees the two inside triangles formed are right triangles with angles 30,60 and 90 degrees.
Play around drawing lines and you will see this.....good luck