The Pentagon belongs to the group of polygons. A polygon is a two-dimensional geometrical shape that is made of straight lines. A polygon can be any two- dimensional shape. There are many examples of geometrical shapes that can be grouped under polygons such as triangle, quadrilateral, pentagon, hexagon, heptagon, octagon and nonagon. Every shape is named according to the number of sides it contains.
TYPES OF POLYGON
Triangle: A triangle has three sides, and the sum of its interior angles measuring 180 degrees.
Quadrilateral: A quadrilateral has four sides, and the sum of its interior angles is 360 degrees.
Pentagon: A Pentagon has five sides, and the sum of its interior angles is 540 degrees.
Hexagon: A Hexagon has six sides. and the sum of its interior angles is 720 degrees.
Heptagon: A Heptagon has seven sides, and the sum of its interior angles is 900 degrees.
Octagon: An Octagon has eight sides, and the sum of its interior angles is 1080 degrees.
Nonagon: A Nonagon has nine sides, and the sum of its interior angles is 1260 degrees.
In a regular polygon, the angles are all equal, and sides are also equal to each other. Its interior angles measure 108 degrees, and exterior angles measure 72 degrees. It has an area of 1.7204774 x s² approximately. Here “s” stands for equal-sided Polygon.
- The general rule for a Polygon is that the sum of its interior angles is equal to 180 multiplied by (n-2) degrees, n being the number of sides – 180 x (n-2).
- In a regular Polygon, the measure of each angle is equal to 180 degrees multiplied by (n-2) divided by n, where n is the number of sides – 180 x (n-2) / n.
A Pentagon consists of five closed sides. There are different types of Pentagon, namely Regular, Irregular, Concave and Convex Pentagon. When an additional side is added to an already existing Pentagon, then the addition of 180 degrees is added to the total sum. For example, when an additional side is added to a triangle of 180 degrees, it becomes a Quadrilateral (4 sides) with a sum of 360 degrees. The sum of all interior angles of a Pentagon is 540 degrees. There are five diagonals in it.
In a regular pentagon, the sides are congruent; that is, the sides are of the same length. The interior angles are also congruent, which means they measure the same angle.
In order to find the interior angles in a Pentagon, divide the sum of all the angles of the Pentagon by the number of angles.
Therefore, 540/5 = 180
This implies that the interior angle of a regular Pentagon is 108 degrees.
CENTRAL ANGLE: In order to find out the central angle of a regular Pentagon, there is a circle to be drawn in the middle of it. It is a well-known fact that a circle is 360 degrees around. Since the Pentagon has five sides, divide the 360 degrees by five.
Therefore, 360/5 =72 degrees.
This implies that the central angle of a Pentagon is equal to 72 degrees.
PENTAGON AND RIGHT ANGLE: It is understood that a Pentagon has five sides. Each interior angle of a Pentagon is 108 degrees. Therefore, It has no right angles. If a Pentagon has to have any right angles, then it has to be uneven because the sum of interior angles in a Pentagon is 540 degrees.
An irregular Pentagon has three right angles at most.
CONVEX AND CONCAVE PENTAGON
In a Convex Pentagon, all the vertices are pointed outwards, and in a concave pentagon, at least one of the vertices is pointed inside.
After reading this article you’ll find that calculating the angles of a pentagon is not quite that difficult. It all comes down to knowing your concepts well and then you can easily solve any geometric problems.