Find the sum of the measures of the interior angles of a convex 16-gon. The sum of the measures of the interior angles is ____°.
Understand the Problem
The question is asking to find the sum of the measures of the interior angles of a convex polygon with 16 sides (16-gon). This can be calculated using the formula (n - 2) * 180°, where n is the number of sides.
Answer
The sum of the measures of the interior angles is $2520^\circ$.
Answer for screen readers
The sum of the measures of the interior angles is $2520^\circ$.
Steps to Solve
- Identify the number of sides (n)
In this case, the polygon is a 16-gon, so $n = 16$.
- Apply the interior angle sum formula
The formula for the sum of the interior angles of a convex polygon is given by:
$$(n - 2) \times 180^\circ$$
- Calculate using the formula
Substitute $n = 16$ into the formula:
$$(16 - 2) \times 180^\circ$$
- Simplify the expression
Calculate $16 - 2$ first:
$$14 \times 180^\circ$$
- Multiply to find the sum of the interior angles
Now, perform the multiplication:
$$14 \times 180 = 2520^\circ$$
The sum of the measures of the interior angles is $2520^\circ$.
More Information
The formula for the sum of the interior angles is derived from the fact that any polygon can be divided into $(n - 2)$ triangles, and since each triangle has a sum of angles equal to $180^\circ$, it applies to any convex polygon.
Tips
- Forgetting to subtract 2 from the number of sides before multiplying by 180.
- Miscalculating basic arithmetic, such as the multiplication step.
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