How to find the interior angle of a regular polygon?
Understand the Problem
The question is asking how to calculate the interior angle of a regular polygon. To solve this, we need to use the formula for the interior angle, which is derived from the number of sides in the polygon.
Answer
The interior angle of a regular hexagon is $120^\circ$.
Answer for screen readers
The interior angle of a regular polygon with 6 sides (hexagon) is $120^\circ$.
Steps to Solve
- Identify the formula for the interior angle
The formula to calculate the interior angle of a regular polygon with ( n ) sides is given by:
$$ \text{Interior Angle} = \frac{(n - 2) \times 180^\circ}{n} $$
- Substitute the value of ( n )
If you know the number of sides ( n ), substitute that value into the formula. For example, if the polygon is a hexagon (which has 6 sides), we substitute ( n = 6 ):
$$ \text{Interior Angle} = \frac{(6 - 2) \times 180^\circ}{6} $$
- Calculate the angle
Now perform the operations in the equation:
First, calculate ( (6 - 2) ):
$$ 6 - 2 = 4 $$
Now substitute that back into the equation:
$$ \text{Interior Angle} = \frac{4 \times 180^\circ}{6} $$
Next, multiply:
$$ 4 \times 180^\circ = 720^\circ $$
Now divide by 6:
$$ \text{Interior Angle} = \frac{720^\circ}{6} = 120^\circ $$
The interior angle of a regular polygon with 6 sides (hexagon) is $120^\circ$.
More Information
The formula for the interior angle of a polygon helps us understand the relationship between the number of sides and the size of each angle. The more sides a regular polygon has, the larger each interior angle will be.
Tips
- Forgetting to subtract 2 from the number of sides before multiplying by 180 degrees. Always remember that the formula involves ( (n - 2) ).
- Incorrectly calculating the basic arithmetic operations; review basic operations to ensure accurate results.
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