(1) Easily proved using sine rule.

(2)

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3) The outer angles are the same as the angles in the triangles r, s and t.

(4) There is much more to discover but this leaves the problem very open. For example there are the recurrence relations, or the repeating angles in the trapezia , or the tessellation of the plane twice with the tiles remaining after all the squares are removed or tessellations suggested by this diagram. vecten with tesellation