Honey bee nests, called honeycombs are constructed to form hexagonal grids as shown below: assuming cells to be regular hexagons of same size, answer the following questions: (i) what is the sum of all interior angles of the hexagonal cells. (ii) find the value of each interior angle of the hexagonal cells. (iii) what is the sum of all interior angles of the hexagon. find the number of diagonals that can be drawn in a hexagonhello everyone how are you all​

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Explanation: In fact the bees simply make cells made of wax that are circular in cross-section. These circular cells are packed together like a layer of bubbles. The wax is softened by the heat of the bees’ bodies and then gets pulled into hexagonal cells by surface tension at the junctions where three walls meet. A regular geometric array of identical cells with simple polygonal cross-sections can take only one of three forms: triangular, square or hexagonal. Of these only hexagons can divide up the space using the smallest wall area. If we interrupt honeybees by smoking them out of the hive we can find that the most recently built cells have a circular shape, whereas those just a little older have developed into hexagons. The worker bees heat the wax with their bodies until it reaches about 45 degree celsius and flows like a viscous liquid. Therefore hexagons would result automatically from the pressure of each bee trying to make its cell as large as possible.

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