Eight triangles of equal size form a regular octagon.
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triangles
There are 4 triangles that make up a pyramid. 4 on the sides and on the bottom a square or rectangle.
Many different types, but mostly equilateral triangles.
An octagonal pyramid has 9 vertices. The base of this shape is an octagon, which will give it 8 vertices when the triangles that form the sides are considered. Those triangles will lead up to the apex (top) of the pyramid, and that will be the 9th vertex.
540 degrees. you figure it out by seeing how many triangles you can make in the polygon (without crossing lines), and, because triangles equal 180 degrees, you multiply 180 times how many triangles you can make.