The measure of angle EBF is 80° .
In the question ,
it is given that ,
point A, B and C lie on a straight line .
and G , B and F lie on a different straight line .
angle GBA = 24° so ,
GBA + GBC = 180° ...because linear pair
So , GBC = 180 - 24 = 156°
angle CBF = 24° ......because vertically opposite angles are equal .
from the figure , we see that angle GBC and angle ABF are vertically opposite angles , so ,
156° = ABE + EBF .....(1)
Since the line AC and DF are parallel and BE is the transversal
So , angle DEB + angle ABE = 180°
104° + ABE = 180°
ABE = 180-104
ABE = 76°
Substituting ABE = 76° in the equation (1) ,
we get ,
156 = 76+ EBF
EBF = 156 - 76
EBF = 80°
Therefore , The measure of angle EBF is 80° .
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