Name the regular polygon that has six sides of equal length and six angles of equal measure.hexagonoctagonheptagonnonagon

The polygon you are describing is a hexagon.

Explanation

A hexagon is defined as a six-sided polygon with equal side lengths and equal angles. It can be classified as a regular hexagon when all sides and angles are identical. In a regular hexagon, each interior angle measures 120 degrees, and the total sum of all interior angles is calculated using the formula:

$\text{Sum of Interior Angles} = (n - 2) \times 180^\circ$

where $n$ is the number of sides. For a hexagon, $n = 6$:

$(6 - 2) \times 180^\circ = 4 \times 180^\circ = 720^\circ$

This confirms the interior angle measure and ensures that any regular hexagon meets the required criteria.

The other options you've provided—octagon (8 sides), heptagon (7 sides), and nonagon (9 sides)—do not meet the 6-sided requirement. Therefore, the answer is:

Final Answer

Hexagon