Interior and Exterior Angles of Polygons Worksheet Write your answer on the pace provided. Round to the nearest hundredth when applicable. I. Determine the sum of the interior angles for each polygon. $$ \begin{array}{lll} ext { 1) } & ext { 2) } 17 ext {-gon } & ext { (3) } 23 ext {-gon }\end{array} $$

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Interior and Exterior Angles of Polygons Worksheet Write your answer on the pace provided. Round to the nearest hundredth when applicable. I. Determine the sum of the interior angles for each polygon. $$ \begin{array}{lll}	ext { 1) } & 	ext { 2) } 17 	ext {-gon } & 	ext { (3) } 23 	ext {-gon }\end{array} $$

UpStudy AI · Accepted Answer

To determine the sum of the interior angles of a polygon, we can use the formula:

$$
S = (n - 2) \times 180
$$

where $$ S $$ is the sum of the interior angles and $$ n $$ is the number of sides (or vertices) of the polygon.

Let's apply this formula to the given polygons:

1. **For the 17-gon:**
   - Here, $$ n = 17 $$.
   - Using the formula:
   $$
   S_{17} = (17 - 2) \times 180
   $$

2. **For the 23-gon:**
   - Here, $$ n = 23 $$.
   - Using the formula:
   $$
   S_{23} = (23 - 2) \times 180
   $$

Now, let's calculate these values.

### Calculation Steps

1. Calculate $$ S_{17} $$:
   $$
   S_{17} = (17 - 2) \times 180 = 15 \times 180
   $$

2. Calculate $$ S_{23} $$:
   $$
   S_{23} = (23 - 2) \times 180 = 21 \times 180
   $$

Now, I will perform these calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(23-2\right)\times 180$$
- step1: Subtract the numbers:
  $$21\times 180$$
- step2: Multiply the numbers:
  $$3780$$
Calculate or simplify the expression $$ (17 - 2) * 180 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(17-2\right)\times 180$$
- step1: Subtract the numbers:
  $$15\times 180$$
- step2: Multiply the numbers:
  $$2700$$
The calculations yield the following results:

1. **For the 17-gon:**
   $$
S_{17} = 2700 \text{ degrees}
   $$

2. **For the 23-gon:**
   $$
S_{23} = 3780 \text{ degrees}
   $$

### Summary of Results
- The sum of the interior angles of a 17-gon is **2700 degrees**.
- The sum of the interior angles of a 23-gon is **3780 degrees**.
- The sum of the interior angles for a 17-gon is 2700 degrees. - The sum of the interior angles for a 23-gon is 3780 degrees.

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