How many degrees are in a decagon?
Understand the Problem
The question is asking for the total number of degrees in the interior angles of a decagon, which is a polygon with ten sides. The approach to solve this involves using 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 total number of degrees in the interior angles of a decagon is $1440$.
Answer for screen readers
The total number of degrees in the interior angles of a decagon is 1440.
Steps to Solve
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Identify the number of sides in the decagon
A decagon has 10 sides. So, we have $n = 10$. -
Use the formula for the sum of interior angles
We can use the formula for the sum of interior angles of a polygon, which is given by:
$$ \text{Sum of interior angles} = (n - 2) \times 180 $$
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Plug in the number of sides into the formula
Substituting $n = 10$ into the formula, we have:
$$ \text{Sum of interior angles} = (10 - 2) \times 180 $$
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Calculate the value
Now we simplify and calculate:
$$ \text{Sum of interior angles} = 8 \times 180 = 1440 $$
The total number of degrees in the interior angles of a decagon is 1440.
More Information
The decagon is a fascinating geometric shape, and knowing how to calculate the sum of its interior angles can help in various applications, including architecture and design. The concept of interior angles also plays a significant role in understanding more complex shapes.
Tips
- Miscounting the sides: It's easy to confuse a decagon with other polygons like a pentagon or hexagon; make sure you remember that a decagon has 10 sides.
- Incorrect application of the formula: Ensure you subtract 2 from the number of sides first before multiplying by 180.
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