Question

How many sides does a pentagon have?
A. 2
B. 5
C. 6
D. 7

Answer 1

Hint: We first try to define the concept of a n-sided polygon. We also find the relation between its sides, angles, and vertices. We place the value of 5 in place of n to find the pentagon. We also define the concept of a regular polygon and regular pentagon.

Complete step-by-step solution:
The pentagon is a 5-sided polygon. In general, a polygon is termed an n-sided polygon.
The number of sides of a polygon is equal to the number of vertices and number of angles.
Therefore, the pentagon has 5 vertices and 5 angles.

The lengths can be different from each other and the same goes for the angles. They are not bound to be equal. But if they are equal then both of them go together to be equal. In that case, the polygon is called a regular polygon.
The correct option is B.

Note: In case of a regular polygon the value of the interior angles is ${\displaystyle \frac{\pi (n-2)}{n}}$ and the exterior angle is ${\displaystyle \frac{2\pi }{n}}$.The smallest polygon is a triangle with 3 sides. So, option (a) can be eliminated. We must know what options (c) and (d) indicate. A polygon having six sides is a hexagon and the one having 7 sides is a heptagon.