The intersection of the bisectors of the angles.
(Sorry _ my original answer, the bisectors of the sides, was clearly wrong.)
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Put one angle of each triangle at the center of the hexagon.
27 triangles.27 triangles.27 triangles.27 triangles.
Yes, draw the lines from the obtuse angles to the center of the line opposite from it.
Triangles without right angles are:- Scalene triangles Obtuse triangles Isosceles triangles Equilateral triangles
Triangles are equilateral triangles only when all of their 3 sides are equal in lengths.