Bunuel wrote:

Official Solution:

A regular pentagon is inscribed in a circle. If \(A\) and \(B\) are adjacent vertices of the pentagon and \(O\) is the center of the circle, what is the value of \(\angle OAB\) ?

A. 48 degrees

B. 54 degrees

C. 72 degrees

D. 84 degrees

E. 108 degrees

\(\angle OAB = \frac{180 - \angle BOA}{2} = \frac{(180 - \frac{360}{5})}{2} = 54\) degrees.

Answer: B

Hi bunuel,

I'd appreciate your help understanding this solution better.

To arrive at 360/5 for angle BOA, it looks like you've assumed the radii from each of the pentagon's vertices to the center divide the 360 degrees into 5 equal parts. Is this allowed? What if the pentagon had unequal sides. Wouldn't that vary the angles subtended at the center?

My geometry is not great. If I've made any incorrect assumptions above, please let me know.