Question

Find the interior angle sum for each polygon. Round your answer to the nearest tenth if necessary.



Question 12 options:

360


1080


720


900

Answer 1

To find the interior angle sum of a polygon, you can use the formula:

\[
\text{Sum of interior angles} = (n - 2) \times 180
\]

where \( n \) is the number of sides of the polygon.

From the options provided (360, 1080, 720, 900), we can identify the possible polygons:

1. **360 degrees**: This corresponds to a triangle (3 sides).
\[
(3 - 2) \times 180 = 1 \times 180 = 180 \text{ (Not an option)}
\]

2. **720 degrees**: This corresponds to a hexagon (6 sides).
\[
(6 - 2) \times 180 = 4 \times 180 = 720 \text{ (This is an option)}
\]

3. **900 degrees**: This corresponds to a heptagon (7 sides).
\[
(7 - 2) \times 180 = 5 \times 180 = 900 \text{ (This is an option)}
\]

4. **1080 degrees**: This corresponds to an octagon (8 sides).
\[
(8 - 2) \times 180 = 6 \times 180 = 1080 \text{ (This is an option)}
\]

Among the options listed, the possible sums of interior angles are:

- 720 degrees (for a hexagon)
- 900 degrees (for a heptagon)
- 1080 degrees (for an octagon)

You would choose the specific polygon based on the context given in the question. But in terms of interior angle sums:
- **Hexagon**: 720 degrees
- **Heptagon**: 900 degrees
- **Octagon**: 1080 degrees

To summarize, all listed options have valid corresponding polygons:

- 360: Not valid for a polygon
- 720: Hexagon
- 900: Heptagon
- 1080: Octagon

If you need the sum of interior angles for a specific polygon, let me know the number of sides, and I can provide the corresponding sum.