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Points $A,$ $B,$ and $C$ are placed on a circle centered at $O$ as in the following diagram:

 

 

If AC = BC and angle OAC = 18 degrees then how many degrees are in angle AOB?

 Jun 29, 2018
 #1
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Draw  radius OC

 

And since  OC = OA, then angles OCA  and OAC  are equal 

 

Then angle  COA  =  180   - 18  -18 = 180  - 36  = 144°

 

And by symmetry, angle BOC = 144°

 

So angle AOB  = 360  - 144 - 144  = 360 - 288  = 72°

 

 

cool cool cool

 Jun 29, 2018

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