Question 44

Mathematics Basic Geometry Medium

In which of the following regular polygons, the number of diagonal is equal to number of sides?

(A) Pentagon
(B) Square
(C) Octagon
(D) Hexagon
View Dynamic Solution & Explanation
Correct Solution: Option A

Step-by-step Solution:

Number of diagonals in a polygon \(={ }^{n} C_{2}-n=n\) \[\] \(\Rightarrow{ }^{n} C_{2}=2 n\) \[\] \(\Rightarrow \frac{n(n 1)}{2}=2 n\) or \(n=5\). Thus the polygon is a pentagon.\[\]Choice (a)\[\]