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A shape with no sides next to each other would be a one sided shape, ie, a circle.
Each team plays 7 matches, but each match involves two teams so the total is (8 x 7)/2 ie 28
Consider the square ABCD whose diagonals, AC and BD, meet at X.AB is parallel to DC and AC intercepts them. Therefore <BAX = <DCX. AB is parallel to DC and BD intercepts them. Therefore <ABX = <CDX. AB = CD. Therefore triangle ABX is congruent to triangle CDX (SAS). So AX = XC ie X is the midpoint of AC and BX = XB ie X is the midpoint of BD. ie the diagonals bisect each other.
The only numbers that are consecutive and prime (ie. they are counting numbers greater than 1 that follow each other and can only be divided by themselves and 1) are;23
Total of interior angles 180 x 7 - 360 ie 900. Total of known angles 570 Balance 330 Each remaining angle 165o