A regular polygon with 8 sides has an angle x. What is the value of x?
Understand the Problem
The question is asking us to find the measure of an interior angle (x) of a regular polygon with 8 sides (an octagon). To solve this, we will use the formula for the interior angle of a regular polygon, which is given by (n-2) * 180/n, where n is the number of sides.
Answer
The measure of each interior angle of a regular octagon is $135$ degrees.
Answer for screen readers
The measure of each interior angle of a regular octagon is $135$ degrees.
Steps to Solve
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Identify the number of sides The regular polygon we are working with is an octagon, which has 8 sides. Therefore, we have $n = 8$.
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Apply the formula for the interior angle We will use the formula for finding the measure of an interior angle, which is given by:
$$ \text{Interior Angle} = \frac{(n - 2) \times 180}{n} $$
Plugging in our value for $n$:
$$ \text{Interior Angle} = \frac{(8 - 2) \times 180}{8} $$
- Calculate the value First, simplify $(8 - 2)$:
$$ \text{Interior Angle} = \frac{6 \times 180}{8} $$
Now multiply $6 \times 180$:
$$ 6 \times 180 = 1080 $$
So now we have:
$$ \text{Interior Angle} = \frac{1080}{8} $$
Now, divide $1080$ by $8$:
$$ \text{Interior Angle} = 135 $$
Thus, the measure of each interior angle of a regular octagon is $135$ degrees.
The measure of each interior angle of a regular octagon is $135$ degrees.
More Information
A regular octagon is a polygon with 8 equal sides and 8 equal angles. The interior angle of $135$ degrees allows for a regular shape, making it symmetrical and aesthetically pleasing.
Tips
- A common mistake is forgetting to subtract 2 from the number of sides before multiplying by 180. Always remember the formula structure!
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