Find the sum of the interior angle measures in a nonagon. (Just write the number)
Understand the Problem
The question is asking to calculate the sum of the interior angles of a nonagon, which is a polygon with nine sides. The formula for the sum of the interior angles of a polygon is (n-2) * 180°, where n is the number of sides.
Answer
1260
Answer for screen readers
1260
Steps to Solve
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Identify the number of sides
A nonagon has 9 sides, so we set ( n = 9 ). -
Substitute into the formula
We use the formula for the sum of the interior angles given by:
$$ \text{Sum of interior angles} = (n-2) \times 180° $$
Substituting ( n = 9 ):
$$ \text{Sum of interior angles} = (9-2) \times 180° $$
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Calculate the difference
Calculate ( 9 - 2 ):
$$ 9 - 2 = 7 $$ -
Multiply by 180°
Now, multiply by 180°:
$$ \text{Sum of interior angles} = 7 \times 180° $$ -
Perform the multiplication
Finally, compute ( 7 \times 180° ):
$$ 7 \times 180° = 1260° $$
1260
More Information
The sum of the interior angles of a nonagon is 1260°. Each interior angle can be calculated by dividing the sum by the number of angles (9 in this case) to find the measure of each angle in a regular nonagon.
Tips
- Incorrectly applying the formula: Always remember to subtract 2 from the number of sides before multiplying by 180°.
- Forgetting to use the correct number of sides: Ensure you are using the right value for ( n ); in this case, it should be 9 for a nonagon.
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