use animation to illustrate the interior angles of hexagon
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Welcome! Today we'll explore the interior angles of a hexagon. A hexagon is a polygon with six sides and six vertices. Each vertex has an interior angle, and we'll discover how these angles relate to each other.
Now let's highlight each interior angle of the hexagon. An interior angle is formed where two adjacent sides meet at a vertex. We can see that our hexagon has six interior angles, one at each vertex labeled A through F.
Now we'll select vertex A and draw diagonals from it to all non-adjacent vertices. From vertex A, we can draw diagonals to vertices C, D, and E. Notice that we don't draw to adjacent vertices B and F, as those are already connected by the sides of the hexagon.
The diagonals have divided our hexagon into exactly four triangles. We know that each triangle has interior angles that sum to 180 degrees. Since we have four triangles, the total sum of all angles is 4 times 180 degrees, which equals 720 degrees.
Therefore, the sum of all interior angles of a hexagon is 720 degrees. This follows the general formula for any polygon: n minus 2, times 180 degrees, where n is the number of sides. For a hexagon with 6 sides, we get 6 minus 2, times 180, which equals 720 degrees.