Question

Find the sum of the internal angels and the sum of the external angles of a regular polygon.

Answer 1

Just tell me the answer

Answer 2

So what's the sum

Answer 3

To find the sums of internal and external angles of a regular polygon, let's define \( n \) as the number of sides of the polygon.

### Sum of Internal Angles
The formula for the sum of the internal angles \( S_i \) of a polygon with \( n \) sides is given by:

\[
S_i = (n - 2) \times 180^\circ
\]

### Sum of External Angles
The sum of the external angles \( S_e \) of any polygon is always:

\[
S_e = 360^\circ
\]

### Summary
- The sum of the internal angles of a regular polygon with \( n \) sides is \( (n - 2) \times 180^\circ \).
- The sum of the external angles of any polygon, irrespective of the number of sides, is always \( 360^\circ \).

Thus, for a regular polygon, the results are:

- Sum of internal angles: \( (n - 2) \times 180^\circ \)
- Sum of external angles: \( 360^\circ \)

Answer 4

The sum of the internal angles of a regular polygon is \( (n - 2) \times 180^\circ \), and the sum of the external angles is always \( 360^\circ \).

Answer 5

The sum of the internal and external angles of a polygon can be calculated as follows:

1. **Sum of Internal Angles**: \( S_i = (n - 2) \times 180^\circ \)
2. **Sum of External Angles**: \( S_e = 360^\circ \)

So, the total sum of the internal and external angles is:

\[
S = S_i + S_e = (n - 2) \times 180^\circ + 360^\circ
\]

This simplifies to:

\[
S = (n - 2) \times 180^\circ + 360^\circ = (n - 2) \times 180^\circ + 2 \times 180^\circ = n \times 180^\circ
\]

Therefore, the total sum of the internal and external angles of a polygon with \( n \) sides is:

\[
\text{Total Sum} = n \times 180^\circ
\]

For any polygon with \( n \) sides, the sum of its internal and external angles is \( n \times 180^\circ \).