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In the diagram, AD=BD=CD and angle BCA = 40 degrees. What is the measure of angle BAC?

 Feb 24, 2019
edited by Lightning  Feb 24, 2019
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Since AD = DC....then angles CAD and  ACD are equal

 

And angle ACD = 40 = angle CAD

 

So....angle  CDA =  180 - 40 - 40 =  100

 

So angle ADB = 180 - 100 =  80

 

And BD = BA.....so angles BAD and ABD are equal

 

So angle BAD =   [ 180 - angle ADB ] / 2 =  [ 180 - 80] / 2 = 100/ 2 = 50

 

So angle BAC = angle CAD + angle BAD  =  40 + 50  =  90°

 

 

cool cool cool

 Feb 24, 2019

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