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If angle BOA = 30 degrees and angle BCO = 40 degrees, then find angle AOC.

 

 Feb 20, 2020
 #1
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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

 

 

cool cool cool

 Feb 20, 2020

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