If angle BOA = 30 degrees and angle BCO = 40 degrees, then find angle AOC.
+128406 I think you must mean that angle BAO = 30°
The sum of the interior angles in quadrilateral AOCB = 360°
And since angle ABC is inscribed....it will = (1/2) central angle AOC
Call central angle AOC = x so angle ABC = (1/2)x
Then in the interior of AOCB obtuse angle AOC = 360 - x
So we have that
30 + 40 + (360 - x) + (1/2)x = 360 simplify
430 - x + (1/2)x = 360
430 - 360 - (1/2)x = 0
70 = (1/2)x multiply through by 2
140° = x = central angle AOC
