Find the size of an interior angle for a decagon.
Understand the Problem
The question is asking to calculate the size of an interior angle for a decagon, which is a polygon with ten sides. To solve this, we will use the formula for calculating the interior angle of a polygon based on the number of sides.
Answer
The size of each interior angle for a decagon is $144$ degrees.
Answer for screen readers
The size of each interior angle for a decagon is $144$ degrees.
Steps to Solve
-
Determine the formula for interior angles of a polygon
The formula to find the measure of each interior angle of a regular polygon is given by:
$$ \text{Interior Angle} = \frac{(n-2) \times 180}{n} $$
where ( n ) is the number of sides. -
Identify the number of sides in a decagon
A decagon has 10 sides, so we set ( n = 10 ). -
Substitute the value into the formula
Substituting ( n = 10 ) into the formula:
$$ \text{Interior Angle} = \frac{(10-2) \times 180}{10} $$ -
Calculate the expression
First, simplify the expression in the parentheses:
$$ (10-2) = 8 $$
Now substitute back to calculate:
$$ \text{Interior Angle} = \frac{8 \times 180}{10} $$ -
Perform the multiplication and division
Calculate ( 8 \times 180 = 1440 ), then divide by ( 10 ):
$$ \text{Interior Angle} = \frac{1440}{10} = 144 $$
The size of each interior angle for a decagon is $144$ degrees.
More Information
In a regular decagon, each of the ten angles measures the same, which is $144$ degrees. This property is true for all regular polygons where the interior angles are equal.
Tips
- Mistaking the number of sides or incorrectly substituting the value of ( n ).
- Forgetting to subtract 2 from ( n ) in the formula.
- Confusing between interior and exterior angles.
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