Answer:
[tex]1,530^o[/tex]
Step-by-step explanation:
we know that
The formula to calculate the sum of the interior angles in a convex polygon is equal to
[tex]S=(n-2)180^o[/tex]
where
n is the number of sides of the polygon
Remember that the number of sides n must be a whole number
Verify each case
case 1) we have
[tex]S=1,530^o[/tex]
Find the number of sides n
substitute in the formula
[tex]1,530^o=(n-2)180^o[/tex]
[tex]n=10.5\ sides[/tex]
The number of sides is not a whole number
therefore
The given number cannot be the sum of the measures of the interior angles of a convex polygon
case 2) we have
[tex]S=3,420^o[/tex]
Find the number of sides n
substitute in the formula
[tex]3,420^o=(n-2)180^o[/tex]
[tex]n=21\ sides[/tex]
The number of sides is a whole number
therefore
The given number can be the sum of the measures of the interior angles of a convex polygon
case 3) we have
[tex]S=6,480^o[/tex]
Find the number of sides n
substitute in the formula
[tex]6,480^o=(n-2)180^o[/tex]
[tex]n=38\ sides[/tex]
The number of sides is a whole number
therefore
The given number can be the sum of the measures of the interior angles of a convex polygon
case 4) we have
[tex]S=4,500^o[/tex]
Find the number of sides n
substitute in the formula
[tex]4,500^o=(n-2)180^o[/tex]
[tex]n=27\ sides[/tex]
The number of sides is a whole number
therefore
The given number can be the sum of the measures of the interior angles of a convex polygon
