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 Two lines l and m intersect at O at an angle of 38˚. Let A be a point inside the acute angle formed by l and m. Let B and C be the reflections of A over lines l and m, respectively. Find the number of degrees in angle BAC.

 Dec 2, 2020
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See the  following image  :

 

 

B is  point A  reflected over  one of the lines  and C  is  the reflection of A over the other line

 

Consider FCAB

Angle  CFB = Angle FBA  = Angle GHO = Angle AEG  = Angle CEG =  90°

Angle  OGH = 90 - 38 =  52°  = Angle EGC

So angle ECG  = 90  - 52  =  38°= angle ACF

 

Then the sum of  the interior angles of FCAB  =  360

 

So

 

angle BAC  = 360  -  angle FBA - angle CFB  - angle  ACF

 

angle  BAC  = 360  - 90  - 90 - 38 =  142°   [ supplemental to the original 38° angle  ]

 

 

cool cool cool

 Dec 2, 2020

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