How many degrees are there in each angle of a regular hexagon?
a) 60 degrees
b) 90 degrees
c) 120 degrees
d) 180 degrees?
The correct answer and explanation is:
The correct answer is c) 120 degrees.
A regular hexagon is a polygon with six sides of equal length and six angles of equal measure. To calculate the measure of each interior angle of a regular hexagon, we can use the formula for the interior angle of a regular polygon: Interior Angle=(n−2)×180∘n\text{Interior Angle} = \frac{(n-2) \times 180^\circ}{n}
Where nn is the number of sides of the polygon. For a hexagon, n=6n = 6. Substituting this into the formula: Interior Angle=(6−2)×180∘6=4×180∘6=720∘6=120∘\text{Interior Angle} = \frac{(6-2) \times 180^\circ}{6} = \frac{4 \times 180^\circ}{6} = \frac{720^\circ}{6} = 120^\circ
Thus, each interior angle of a regular hexagon is 120 degrees.
In a regular hexagon, the sum of the interior angles is calculated as: Sum of Interior Angles=(n−2)×180∘=(6−2)×180∘=4×180∘=720∘\text{Sum of Interior Angles} = (n-2) \times 180^\circ = (6-2) \times 180^\circ = 4 \times 180^\circ = 720^\circ
Since the hexagon is regular, all six interior angles are equal. Therefore, each angle is: 720∘6=120∘\frac{720^\circ}{6} = 120^\circ
This means that every angle inside the regular hexagon measures exactly 120 degrees.
Understanding the properties of a regular hexagon is essential in various fields such as geometry, architecture, and design, where symmetry plays a significant role. The regular hexagon’s 120-degree angles contribute to its unique and highly symmetrical shape, making it suitable for tiling and other applications.