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

or

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

Q: What is the measure of each arc of a circle that is circumscribed about a regular pentagon?

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circumscribed means the polygon is drawn around a circle, and inscribed means the polygon is drawn inside the circle. See related links below for polygon circumscribed about a circle and polygon inscribed in a circle.

the center of a circumscribed circle is called the focus.

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assuming this is a regular pentagon (all five sides are equal length) the center is the intersection of the intersection of perpendicular bisectors of each side and should also be the center of the circle in which it is inscribed

Is equidistant from all points on the circle.

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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.

circumscribed means the polygon is drawn around a circle, and inscribed means the polygon is drawn inside the circle. See related links below for polygon circumscribed about a circle and polygon inscribed in a circle.

If the distance from the centre of the pentagon to a vertex is r cm then the length of the arc is 0.4*pi*r cm

the center of a circumscribed circle is called the focus.

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To circumscribed a circle about a triangle you use the angle. This is to get the right measurements.

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A circumscribed polygon is a polygon all of whose vertices are on the circumference of a circle. The circle is called the circumscribing circle and the radius of the circle is the circumradius of the polygon.

The measure of an exterior angle of an equiangular pentagon is 72 degrees. An equiangular pentagon is a regular pentagon that has five equal sides and five equal angles. An interior angle of a pentagon is equal to 108 degrees.

assuming this is a regular pentagon (all five sides are equal length) the center is the intersection of the intersection of perpendicular bisectors of each side and should also be the center of the circle in which it is inscribed

A triangle has exactly one circumscribed circle.

A polygon which has a circumscribed circle is called a cyclic polygon.All regular simple polygons, all triangles and all rectangles are cyclic.