Question 1119306
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<pre>
The six angles measures are 2x, 3x, 4x, 5x, 6x and 7x,  where x is their common measure.


The sum of interior angles of any n-sided polygon is  (n-2)*180 degrees, therefore


    2x + 3x + 4x + 5x + 6x + 7x = 4*180,    or

    27x = 720

    x = {{{720/27}}} = {{{26}}}{{{2/3}}} degrees.


The greatest angle measure is  7 times {{{26}}}{{{2/3}}} degrees,  or {{{186}}}{{{2/3}}} degrees = {{{560/3}}} degrees.
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Solved.