The interior angle sum of a polygon can be calculated using the formula:

$\text{Interior Angle Sum} = 180^\circ \times (n - 2)$

where $n$ is the number of sides of the polygon. Let's calculate the interior angle sum for polygons with 14, 24, 17, and 8 sides.

1. 14-sided polygon (n = 14):

$\text{Interior Angle Sum} = 180^\circ \times (14 - 2) = 180^\circ \times 12 = 2160^\circ$

2. 24-sided polygon (n = 24):

$\text{Interior Angle Sum} = 180^\circ \times (24 - 2) = 180^\circ \times 22 = 3960^\circ$

3. 17-sided polygon (n = 17):

$\text{Interior Angle Sum} = 180^\circ \times (17 - 2) = 180^\circ \times 15 = 2700^\circ$

4. 8-sided polygon (n = 8):

$\text{Interior Angle Sum} = 180^\circ \times (8 - 2) = 180^\circ \times 6 = 1080^\circ$

So, the interior angle sums are:

• 14-sided polygon: $2160^\circ$
• 24-sided polygon: $3960^\circ$
• 17-sided polygon: $2700^\circ$
• 8-sided polygon: $1080^\circ$

Would you like to know more details or have any questions?

Here are 5 related questions to explore:

1. How do you calculate the measure of a single interior angle in a regular polygon?
2. What is the relationship between the number of sides and the interior angle sum of a polygon?
3. How does the interior angle sum change as the number of sides increases?
4. Can a polygon have an interior angle sum of 720°? If so, how many sides does it have?
5. What is the interior angle of a regular polygon with 12 sides?

Tip: Remember, as the number of sides of a polygon increases, the sum of the interior angles also increases, while the sum of the exterior angles remains constant at $360^\circ$.