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 Geometry: Circles and their properties Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Circles Question 37568: incase you cannot read that it says, In the diagram, a regular hexagon is inscribed in a circle. what is the measure of the inscribed angle ABC?Answer by fractalier(2101)   (Show Source): You can put this solution on YOUR website!Two ways to do this one (at least). The interior angle of any regular polygon is found by x = (180)(N - 2) / N where N = number of sides. Here that is 6, so x = 180(4) / 6 = 120 degrees. Another way is recognizing that an inscribed angle is equal to half the number of degrees it cuts off. The angle cuts off 4/6 of the circle...4/6 of 360 degrees is 240 degrees and half of that is 120 degrees. Either way its's 120 degrees.