Question 1 of 20 - How many sides does a polygon have that has an interior angle sum of 5040°?

The sum of the interior of an n-gon (a polygon with n sides), whether regular or irregular, is 180°×(n-2). So the sum of the interior angles of a triangle is 180°×(3–2) =180°×1 = 180°, the sum of the interior angles of a quadrilateral is 180°×(4–2) = 180°×2 = 360°, the sum of the interior angles of a pentagon is 180°×(5–2) =180°×3 = 540°, the sum of the interior angles of a hexagon is 180°×(6–2) = 180°×4 = 720°, and so on.

Let s be the number of sides of a pentagon the sum of whose interior angles is 5040°.

Then 180°×(s-2) = 5040°.

So, s-2 = 5040°/180° = 28.

So, s = 28+2 = 30.

So, s = 30.

So the polygon has 30 sides.

the answer is 40.

proof: