Final answer:
The question is to find the number of sides of a convex polygon given the sum of its angles minus one angle is 2180 degrees. By using the formula for the sum of the interior angles of a polygon and setting up an equation, it is determined the polygon must have 14 sides. The provided answer choices are incorrect.
Step-by-step explanation:
The question is asking to find the number of sides of a convex polygon given that the sum of all its angles except one is 2180 degrees. We can start by recalling that the sum of the interior angles of a convex polygon with n sides is given by the formula (n-2)×180 degrees.
Since we know the sum of all but one of the angles is 2180 degrees, we can set up the equation (n-2)×180 - x = 2180, where x is the measure of the remaining angle.
However, we also know that each angle in a polygon must be greater than 0 degrees, which means that the remaining angle must also contribute to the total. Therefore, we can simplify our equation to (n-2)×180 = 2180 + x. Since the value of x is unknown but positive, we can ignore it and directly equate (n-2)×180 to 2180 to find the minimum number of sides the polygon could have, assuming the last angle is greater than 0 degrees, as it must be for a convex polygon.
So, our revised equation becomes (n-2)×180 = 2180. Solving for n gives us n = 2180/180 + 2, which simplifies to n = 12 + 2. Therefore, the polygon must have 14 sides. None of the provided options (a. 8, b. 9, c. 10, d. 11) are correct.