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In \(\triangle ABC\), internal angle bisector of \(\angle BAC\) divides \(\triangle ABC\)'s circumcircle into two arcs whose ratio of lengths is \(7:11\). Given that \(\angle ACB = 36°\), find the measure of \(\angle ABC\) in degrees.

 

 Jan 19, 2021
 #1
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Note that minor arc AB  =2 (36°)   = 72°

 

And  arc  ABM  is 7/18 of the  circumference  =  (7/18) * 360   =140°

 

So minor arc BM =   140  -72    =  68°  = 2*angle BAM  =  angle BAC

 

So  angle   ABC  =  180  - 36 -  68  = 76°

 

 

cool cool cool

 Jan 19, 2021
edited by CPhill  Jan 19, 2021
 #2
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//////////////////////////cheeky

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 Jan 24, 2021
edited by Guest  Jan 24, 2021

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