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Angular measure: 2*pi/5 radians or 72 degrees.


Length of arc: 2*r*pi/5 units or 144*r units, where r is the radius.

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Q: What is the measure of each arc of a circle that is circumscribed about a regular pentagon?
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The apothem of a regular pentagon is 10.8 centimeters what is the radius of the circumscribed circle?

The line joining the centre of the pentagon to any vertex is a radius of the circumscribed circle. The angle between such a line and the adjacent apothem is 360/10 = 36 degrees. If the radius is r, then we can now write: cos36 = 10.8/r So r = 10.8/cos36 = 13.350cm. to 3 decimal places.

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