Question

A regular decagon is a polygon with ten sides of equal length. Use complete sentences to design a strategy to determine the sum of the interior angles of a regular decagon. In your final answer, include the sum and all of your calculations.

Answer 1

To determine the sum of the interior angles of a regular decagon, we can use the formula for finding the sum of the interior angles of any polygon. The formula is given by:

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

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

For a decagon, we know that \( n = 10 \) because a decagon has ten sides. Now, we can plug this value into the formula:

1. **Substitute \( n \) into the formula**:
\[
\text{Sum of interior angles} = (10 - 2) \times 180^\circ
\]

2. **Calculate \( 10 - 2 \)**:
\[
10 - 2 = 8
\]

3. **Multiply by 180 degrees**:
\[
\text{Sum of interior angles} = 8 \times 180^\circ
\]

4. **Calculate \( 8 \times 180 \)**:
\[
8 \times 180 = 1440
\]

Thus, the sum of the interior angles of a regular decagon is \( 1440^\circ \).

In summary, by using the formula for the sum of interior angles and substituting the number of sides in a decagon, we find that the total sum of the interior angles is \( 1440^\circ \).