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
Answer for screen readers
The total number of degrees in the interior angles of a nonagon is 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).