What do the angles in a hexagon add up to?
Understand the Problem
The question is asking for the sum of the internal angles of a hexagon. To solve this, we can use the formula for calculating the sum of interior angles of an n-sided polygon, which is given by (n-2) * 180 degrees, where n is the number of sides of the polygon.
Answer
$720^\circ$
Answer for screen readers
The sum of the internal angles of a hexagon is $720^\circ$.
Steps to Solve
-
Identify the number of sides in a hexagon
A hexagon has 6 sides. We can denote the number of sides as $n = 6$. -
Use the formula for the sum of interior angles
The formula to calculate the sum of interior angles of an $n$-sided polygon is:
$$(n - 2) \times 180^\circ$$ -
Substitute the number of sides into the formula
Now, plug in the number of sides into the formula:
$$(6 - 2) \times 180^\circ = 4 \times 180^\circ$$ -
Calculate the product
Now calculate the product:
$$4 \times 180^\circ = 720^\circ$$
The sum of the internal angles of a hexagon is $720^\circ$.
More Information
The sum of the internal angles formula can be used for any polygon. For example, a triangle (3 sides) has a sum of $180^\circ$, and a pentagon (5 sides) has a sum of $540^\circ$. Understanding these relationships helps in geometry.
Tips
- A common mistake is to forget to subtract 2 from the number of sides before multiplying by 180. Always remember to do $n - 2$ first.
- Another mistake is not recognizing the hexagon as a 6-sided polygon. Be sure to correctly identify the shape's properties.
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