Question

How many sides does a polygon with interior angles that total 900° have? Show and explain your work. ​

Answer 1

7 sides

Explanation:

For any convex polygon with n sides, we can use the following formula to determine the sum of the interior angles:

Sum = 180(n - 2)

Since we know that the sum of the interior angles of this problem's polygon is 900°, we can substitute 900 for the sum to find n, the number of sides the polygon has:

Step 1: Substitute 900 for the sum and divide both sides by 180:

(900 = 180(n - 2)) / 180

5 = n - 2

Step 2: Add 2 to both sides to determine the total number of sides, n, the polygon has:

(5 = n - 2) + 2

7 = n

Thus, the polygon (which we now know is a heptagon) has 7 sides.