What is the sum of the interior angles of a heptagon?
Understand the Problem
The question is asking for the formula or calculation to determine the sum of the interior angles of a heptagon, which is a seven-sided polygon. To find this, we will use the formula (n-2) * 180, where n is the number of sides.
Answer
The sum of the interior angles of a heptagon is \( 900 \) degrees.
Answer for screen readers
The sum of the interior angles of a heptagon is ( 900 ) degrees.
Steps to Solve
- Identify the number of sides (n)
For a heptagon, the number of sides is $n = 7$.
- Apply the formula for the sum of interior angles
The formula for calculating the sum of the interior angles of a polygon is given by:
$$ \text{Sum of interior angles} = (n-2) \times 180 $$
Substituting in the value of $n$:
$$ \text{Sum of interior angles} = (7-2) \times 180 $$
- Calculate the result
Now, perform the calculation:
$$ \text{Sum of interior angles} = (5) \times 180 = 900 $$
Thus, the sum of the interior angles of a heptagon is 900 degrees.
The sum of the interior angles of a heptagon is ( 900 ) degrees.
More Information
A heptagon is a polygon with seven sides, and the formula used, $(n-2) \times 180$, can be applied to any polygon to find the sum of its interior angles. For example, a triangle (3 sides) has a sum of ( 180 ) degrees, while a quadrilateral (4 sides) has ( 360 ) degrees.
Tips
- Forgetting to subtract 2 from the number of sides before multiplying by 180. This can lead to an incorrect calculation of the sum of the angles.
- Confusing the formula for the sum of interior angles with the formula for exterior angles, which has a different significance.
