How many sides does a pentagon have?
The correct answer and explanation is:
A pentagon has five sides.
A pentagon is a type of polygon, which is defined as a closed geometric figure made up of straight line segments. The number of sides a polygon has is a key feature in classifying it. The term “pentagon” comes from the Greek word “pente,” meaning five, and “gonia,” meaning angle, thus literally translating to “five angles.” Each side of a pentagon is connected to two other sides, forming a closed shape with five corners or vertices.
The sum of the interior angles of any polygon can be calculated using the formula: Sum of interior angles=(n−2)×180∘\text{Sum of interior angles} = (n – 2) \times 180^\circ
where nn is the number of sides. For a pentagon, substituting n=5n = 5 into the formula gives: Sum of interior angles=(5−2)×180∘=3×180∘=540∘\text{Sum of interior angles} = (5 – 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ
This means the sum of all five interior angles of a pentagon is 540 degrees. In a regular pentagon, where all sides and angles are equal, each interior angle is: 540∘5=108∘\frac{540^\circ}{5} = 108^\circ
A regular pentagon has equal-length sides, and each of its interior angles measures 108 degrees. It is one of the most common polygons studied in geometry due to its symmetry and frequent appearance in various fields, such as architecture and art.
In summary, a pentagon always has five sides, and its geometry leads to specific calculations for the sum of its interior angles.