Question

The sum of the measures of the interior angles of a polygon with n sides is s. Without using n in your answer, express in terms of s the sum of the measures of the angles of a polygon with:

a. 180 °
b. 360 °
c. (n−2)⋅180 °
d. s °

Answer 1

To express the sum of the measures of the angles of a polygon in terms of s, for 180° it represents a triangle, for 360° a quadrilateral, for (n-2) ×180° it is s itself, and for s° this is directly the given sum.

Step-by-step explanation:

The sum of the measures of the interior angles of a polygon is a function of the number of sides the polygon has. The general formula to calculate this sum is (n-2) ×180°, where n is the number of sides.

In the context of the question:

1. For 180°, this would represent the sum of the angles of a triangle, because a triangle always has angles that add up to 180 degrees.
2. For 360°, this would not correspond to the sum of the interior angles of any polygon, as the minimum sum for a four-sided polygon (quadrilateral) is 360 degrees. So, assuming there's an error and we are to find the sum of angles for a polygon that would give 360 degrees, it would be a quadrilateral.
3. For (n-2) ×180°, this is simply the standard formula restated, so the sum of measures of the angles would be precisely s.
4. For s°, it is assuming the value given is already the sum of the interior angles, so the answer would once again be s.