Question$A B C D E F$ is a regular hexagon. a) What is one inner angle of a regular hexagon? b) Find $\angle C A E$. c) Prove that triangle ACE is equilateral.

Studdy Solution
To prove that triangle $ACE$ is equilateral, note the following: - All sides of the regular hexagon are equal. - Since $A$, $C$, and $E$ are vertices of the hexagon, segments $AC$, $CE$, and $AE$ are sides of the hexagon.
Since $AC = CE = AE$, and each side of the regular hexagon is equal, triangle $ACE$ has all sides equal.
Additionally, $\angle C A E = 60^\circ$, and similarly, $\angle A C E$ and $\angle C E A$ are also $60^\circ$ because each vertex angle in an equilateral triangle is $60^\circ$.
Therefore, $\triangle ACE$ is equilateral.
Solution: a) One inner angle of a regular hexagon is $120^\circ$. b) $\angle C A E = 120^\circ$. c) Triangle $ACE$ is equilateral.