Question 1125767
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Obviously if an algebraic solution is not required, you would solve this quickly with logical analysis.<br>
The number of diagonals in a polygon with 3 sides is {{{(3*0)/2}}} = 0
The number of diagonals in a polygon with 4 sides is {{{(4*1)/2}}} = 2
The number of diagonals in a polygon with 5 sides is {{{(5*2)/2}}} = 5
The number of diagonals in a polygon with 6 sides is {{{(6*3)/2}}} = 9<br>
If the total number of diagonals in two polygons is 7, then the polygons must have 4 and 5 sides.