Find the sum of the measures of the interior angles of a convex 20-gon. The sum of the measures of the interior angles is ____.
Understand the Problem
The question asks to calculate the sum of the interior angles of a convex polygon with 20 sides (20-gon). The formula involves determining the number of sides and applying it to find the total sum of the angles.
Answer
The sum of the measures of the interior angles is \( 3240^\circ \).
Answer for screen readers
The sum of the measures of the interior angles is ( 3240^\circ ).
Steps to Solve
- Identify the formula for the sum of interior angles
The formula to find the sum of the interior angles of a polygon is given by:
$$ S = (n - 2) \times 180 $$
where ( S ) is the sum of the interior angles and ( n ) is the number of sides of the polygon.
- Substitute the number of sides into the formula
For a 20-gon, we substitute ( n = 20 ) into the formula:
$$ S = (20 - 2) \times 180 $$
- Calculate the sum of the interior angles
Now, simplify ( 20 - 2 ) and multiply by 180:
$$ S = 18 \times 180 $$
Now perform the multiplication:
$$ S = 3240 $$
The sum of the measures of the interior angles is ( 3240^\circ ).
More Information
The sum of the interior angles formula is useful for any polygon and helps in geometry problems involving shapes with multiple sides. For a 20-gon, there are many applications in architecture and design where such calculations are necessary.
Tips
- Forgetting to subtract 2: Some might forget that we subtract 2 from the number of sides before multiplying by 180.
- Incorrect multiplication: Be careful to multiply correctly; using a calculator can help prevent simple arithmetic mistakes.
AI-generated content may contain errors. Please verify critical information
