A regular polygon with 3 sides has an angle x. What is the value of x?
Understand the Problem
The question is asking for the measure of an interior angle of a regular polygon with 3 sides, which is known as a triangle. To find the value of x, we will use the formula for the interior angle of a regular polygon, which is (n-2) * 180 / n, where n is the number of sides.
Answer
$60^\circ$
Answer for screen readers
The measure of an interior angle of a regular polygon (triangle) is $60^\circ$.
Steps to Solve
- Identify the number of sides (n)
In this case, we have a triangle, which has 3 sides. So, $n = 3$.
- Use the formula for the interior angle
The formula for finding the interior angle of a regular polygon is given by:
$$ \text{Interior Angle} = \frac{(n - 2) \times 180}{n} $$
- Substitute the value of n into the formula
Now, substituting $n = 3$ into the formula:
$$ \text{Interior Angle} = \frac{(3 - 2) \times 180}{3} $$
This simplifies to:
$$ \text{Interior Angle} = \frac{1 \times 180}{3} $$
- Calculate the interior angle
Now, performing the calculation:
$$ \text{Interior Angle} = \frac{180}{3} = 60 $$
So, the measure of the interior angle of a triangle is $60^\circ$.
The measure of an interior angle of a regular polygon (triangle) is $60^\circ$.
More Information
A triangle is the simplest polygon and is the only polygon with three sides. It is also the foundation of many geometric concepts. Each interior angle in an equilateral triangle measures $60^\circ$, making all its angles equal.
Tips
- Forgetting the formula: Some may forget to apply the correct formula for the interior angles of a polygon. Always remember: $\frac{(n - 2) \times 180}{n}$.
- Not dividing properly: Ensure correct calculations when dividing the product of $(n - 2) \times 180$ by $n$.
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