A regular pentagon is inscribed in a circle. What angle does each side subtend at the centre?

Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

A regular pentagon has 5 equal sides.
These sides become 5 equal chords of the circle.
Therefore, each side subtends the same angle at the centre.
Let each side subtend angle x at the centre.
Then, 5x = 360o                       (complete angle at the centre is 360o)
            x = 72o
Hence, each side of a regular pentagon inscribed in a circle subtends an angle of 72o at the centre.

Answered by  | 4th Jun, 2014, 03:23: PM