# Solution to the Square and a Hexagon Puzzle +-- {.image} [[ASquareandaHexagon.png:pic]] > Two regular polygons. What’s the angle? =-- ## Solution by [[Angle in a Semi-Circle]], [[Angles in the Same Segment]], and angles in a [[Regular Hexagon]] +-- {.image} [[ASquareandaHexagonLabelled.png:pic]] =-- In the diagram above, the orange circle is the [[circumcircle]] of the [[regular hexagon]]. The [[chord]] $A B$ joins opposite vertices so is a [[diameter]] of the circle. Angle $A \hat{G} D$ is a [[right-angle]] and so since the [[angle in a semi-circle]] is a right-angle, $G$ lies on the circle. Then since [[angles in the same segment]] are equal, angle $B \hat{G} D$ is the same as angle $B \hat{A} D$, which is half the [[interior angle]] of a [[regular hexagon]] and so is $60^\circ$.