In triangle ABC, BAC = 78 degrees. The incircle of triangle ABC touches sides BC, AC, and AB at D, E, and F, respectively. Find EDF in degrees.
Let the centor of the incircle = O
Then angles AEO and AFO = 90°
And in quadrilateral AFOE....angle FOE can be found as
90 + 90 +78 + angle FOE = 360
258 + angle FOE = 360
angle FOE = 360 - 258 = 102°
And angle EDF is an inscribed angle in the incircle that subtends the same arc as angle FOE
So...angle EDF = (1/2) 102 = 51°