How many degrees in a decagon?

Understand the Problem

The question is asking about the total number of degrees in a decagon, which is a polygon with ten sides. To find this, we will use the formula for calculating the interior angles of a polygon.

Answer

$1440$

Steps to Solve

Identify the formula for the sum of interior angles of a polygon

The formula to find the sum of the interior angles of a polygon with $n$ sides is given by:

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

where $n$ is the number of sides of the polygon.

Substitute the value for a decagon

Since a decagon has 10 sides, we will substitute $n = 10$ into the formula:

$$ S = (10 - 2) \times 180 $$

Calculate the expression

Now, perform the calculation:

$$ S = 8 \times 180 $$

Final Calculation

Now, calculate $8 \times 180$:

$$ S = 1440 $$

This means the total number of degrees in a decagon is 1440 degrees.

The total number of degrees in a decagon is $1440$.

More Information

A decagon is a polygon with ten sides, and the calculation of the sum of interior angles is a fundamental concept in geometry. Interestingly, as you increase the number of sides in a polygon, the sum of the interior angles increases as well.

Tips

A common mistake is to forget to subtract 2 from the number of sides (i.e., confusing the formula with just $n \times 180$). Always remember to use $(n - 2)$ in the formula.

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