Find the size of an interior angle for a decagon.
Understand the Problem
The question is asking for the calculation of the size of an interior angle of a decagon, which is a ten-sided polygon. To solve it, we will use the formula for finding the interior angle of a polygon.
Answer
The size of an interior angle for a decagon is \( 144^\circ \).
Answer for screen readers
The size of an interior angle for a decagon is ( 144^\circ ).
Steps to Solve
- Understand the formula for interior angles
To find the measure of an interior angle of a polygon, we use the formula: $$ \text{Interior Angle} = \frac{(n - 2) \times 180^\circ}{n} $$ where ( n ) is the number of sides of the polygon.
- Substitute the number of sides for a decagon
Since a decagon has 10 sides, we substitute ( n = 10 ) into the formula: $$ \text{Interior Angle} = \frac{(10 - 2) \times 180^\circ}{10} $$
- Perform the calculation
Now simplify the equation: $$ \text{Interior Angle} = \frac{8 \times 180^\circ}{10} $$ Calculate ( 8 \times 180 = 1440 ): $$ \text{Interior Angle} = \frac{1440^\circ}{10} $$
- Find the final result
Divide 1440 by 10: $$ \text{Interior Angle} = 144^\circ $$
The size of an interior angle for a decagon is ( 144^\circ ).
More Information
Interior angles are important in many fields, including architecture and design. The larger the number of sides in a polygon, the closer each interior angle gets to ( 180^\circ ).
Tips
- Forgetting to subtract 2 from the number of sides: This is crucial since the formula accounts for triangles that can be formed within the polygon.
- Not dividing by the number of sides after calculating the total interior angle sum.
AI-generated content may contain errors. Please verify critical information
