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Two lines l and m intersect at O at an angle of 28 degrees. 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.

Guest Apr 15, 2017
 #1
avatar+7324 
+3

Hmmmmm! This is an interesting one...

Here is a picture:

 

There is a quadrilateral formed in the middle by:

point O, the intersection point of AB and l, point A, and the intersection point of AC and m.

 

The sum of the interior angles in every quadrilateral = 360º

 

Look! We know all 3 angles in the quadrilateral except angle BAC.

 

28º + 90º + m∠BAC + 90º = 360º

m∠BAC = 360º - 90º - 90º - 28º

m∠BAC = 152º

hectictar  Apr 16, 2017
 #2
avatar+90001 
+1

Very impressive, hectictar....!!!!

 

Notice that the selection of point "A"  is irrelevent......the fact that BA  and CA are perpendicular to l and m means that  angle BAC always = 152°.......!!!!

 

 

 

cool cool cool

CPhill  Apr 16, 2017
edited by CPhill  Apr 16, 2017

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