Find the sum of the interior angles of a nonagon.
Understand the Problem
The question is asking how to calculate the sum of the interior angles of a nonagon, which is a polygon with nine sides. To solve 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
The sum of the interior angles of a nonagon is $1260^\circ$.
Answer for screen readers
The sum of the interior angles of a nonagon is $1260^\circ$.
Steps to Solve
-
Identify the number of sides
For a nonagon, the number of sides $n$ is 9. -
Use the formula for the sum of interior angles
We know the formula for finding the sum of the interior angles of a polygon is: $$ \text{Sum of interior angles} = (n - 2) \times 180^\circ $$ -
Substitute the number of sides into the formula
Plugging in the value of $n = 9$: $$ \text{Sum of interior angles} = (9 - 2) \times 180^\circ $$ -
Simplify the expression
Calculate $9 - 2$: $$ 9 - 2 = 7 $$
Now substitute this back into the equation: $$ \text{Sum of interior angles} = 7 \times 180^\circ $$ -
Multiply to find the final answer
Now, calculate: $$ 7 \times 180 = 1260 $$
Therefore, the sum of the interior angles of a nonagon is $1260^\circ$.
The sum of the interior angles of a nonagon is $1260^\circ$.
More Information
The sum of the interior angles formula is general for polygons and is helpful in various geometry problems. A nonagon is significant in geometry and design, and understanding its properties can be essential in advanced mathematical concepts.
Tips
- Confusing the number of sides: Ensure you correctly identify the polygon type.
- Forgetting to subtract 2 from the number of sides in the formula. Double-check the formula before calculating.
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