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In triangle ABC, AX = XY = YB = BC and the measure of angle ABC is 150 degrees. What is the number of degrees in the measure of angle BAC?

 

 Jun 28, 2022
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Since BY = BC

Let  angles BCY and BYC = x = angle BCA 

Then angle YBC =  180  - 2x

And angle XBY =   150 - (180 - 2x) =  2x - 30 = Angle BXY

And since AX = XY

The angles  XAY and XYA are equal

And by the exterior angle theorem, angle BXY =  2* angle  XAY= angle BAC 

2 * angle BAC = angle BXY

2 * angle BAC =   2x - 30

angle BAC = (2x - 30) / 2 =  x - 15

 

So

 

angle BAC +  angle ABC  + angle  BCA = 180

 

(x - 15)   +  ( 150 )  +  (x)  =  180

 

2x +  135  = 180

 

2x =  180 - 135

 

2x  = 45

 

x = 22.5

 

Angle BAC =  22.5 - 15 =    7.5°

 

cool cool cool

 Jun 29, 2022

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