Answer:
Step-by-step explanation:
we know that
The formula to calculate the sum of the interior angles in a convex polygon is equal to
where
n is the number of sides of the polygon
Remember that the number of sides n must be a whole number
<u><em>Verify each case</em></u>
case 1) we have
Find the number of sides n
substitute in the formula
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
Find the number of sides n
substitute in the formula
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
Find the number of sides n
substitute in the formula
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
Find the number of sides n
substitute in the formula
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