question_answer

A regular hexagon is inscribed in a circle with centre O. Then the angle subtended by each side of the square at the centre O is:

A) \[{{80}^{o}}\]                        

B) \[{{90}^{o}}\]

C) \[{{60}^{o}}\]                          

D) \[{{45}^{o}}\]

Correct Answer: C

Solution :

A regular hexagon has 6 sides of equal length. \[\therefore \]Each side subtends the same angle at the centre. \[\therefore \]      \[6{{x}^{o}}={{360}^{o}}\]             \[{{x}^{o}}=\frac{{{360}^{o}}}{6}={{60}^{o}}\Rightarrow x={{60}^{o}}\]