The polygon with an interior angle sum of 540 degrees has 5 sides. This is determined using the formula for the sum of interior angles of a polygon:[tex]Sum \: of \: interior \: angles \: = (n−2) \: ×180° [/tex]where n is the number of sides. Setting this equal to 540:[tex](n−2) \: × \: 180 \: = \: 540[/tex]Dividing both sides by 180:[tex]n \: − \: 2 \: = \: 3[/tex]Adding 2 to both sides:[tex]n \: = \: 5[/tex]Therefore, the polygon is a pentagon with 5 sides[tex].[/tex]