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Segment AD bisects angle BAC. If BD=DA=AC, what is angle AC in degrees?

 Nov 14, 2018
 #1
avatar+107405 
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Don't know what  angle "AC" is...but if you want to know  the angles, we have

 

Because BD  = AD.....then angle ABD  = angle BAD.....let these angle measures  = x

 

And because  AC = AD....then angle ADC = angle ACD.....let these angle measures = y

 

In triangle ABD, using the Exterior Angle Theorem,  angle ADB  =  x + y

In triangle DAC, angle DAC  =  angle BAD  = x

 

So....we have the following system.....

 

x + x + x + y   = 180   ⇒    3x + y  =  180   ⇒   -6x - 2y  = -360   (1)

x + 2y  = 180    (2)

 

Add (1)  and (2)   and we get that

 

-5x  = -180

x  = 36°

 

And using (2)

36 + 2y  = 180

2y  = 144

y = 72°

 

So   angles  ABD, ADB, DAC   = 36°

And angles ADC, ACD   = 72°

And angle ADB  = 36 + 72   =   108°

 

 

 

cool cool cool

 Nov 14, 2018

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