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.
+128448 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 ]
