# The interior angles of a hexagon are #x+2, x-8, x +7, x -3, x+6, and x -4#. What is the value of #x#?

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To find the value of ( x ), you need to sum up the interior angles of the hexagon and set the sum equal to ( 180^\circ ) since the sum of interior angles of a polygon with ( n ) sides is given by ( (n-2) \times 180^\circ ).

Sum of the interior angles of a hexagon ( = (6-2) \times 180^\circ = 720^\circ ).

So, ( (x+2) + (x-8) + (x+7) + (x-3) + (x+6) + (x-4) = 720^\circ ).

Solve this equation for ( x ).

( 6x - 2 = 720^\circ )

( 6x = 722^\circ )

( x = \frac{722^\circ}{6} )

( x = 120.33^\circ )

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