How many degrees are in a nonagon?

Understand the Problem

The question is asking for the total number of degrees in the interior angles of a nonagon, which is a polygon with nine sides. To find this, we can use the formula for the sum of interior angles of a polygon, which is (n - 2) * 180, where n is the number of sides.

Answer

1260 degrees

Steps to Solve

Identify the number of sides in the polygon

For a nonagon, the number of sides $n$ is 9.

Use the formula for the sum of interior angles

The formula to find the sum of the interior angles of a polygon is given by:

$$ \text{Sum of interior angles} = (n - 2) \times 180 $$

Substituting the value of $n$:

$$ \text{Sum of interior angles} = (9 - 2) \times 180 $$

Calculate the difference and multiply

Now, calculate $9 - 2$:

$$ 9 - 2 = 7 $$

Next, multiply by 180:

$$ 7 \times 180 = 1260 $$

State the final result

Thus, the total number of degrees in the interior angles of a nonagon is 1260 degrees.

The total number of degrees in the interior angles of a nonagon is 1260 degrees.

More Information

The sum of the interior angles is an important concept in geometry. It helps in understanding how the angles of different polygons relate to the number of sides they have. This also illustrates the relationship that as the number of sides increases, the sum of the interior angles also increases.

Tips

Forgetting to subtract 2 from the number of sides before multiplying by 180.
Misapplying the formula to the correct polygon (confusing it with other shapes).

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