In triangle ABC, BAC = 78 degrees and ACB = 33 degrees. The incircle of triangle ABC touches sides BC, AC, and AB at D, E, and F, respectively. Find EFD in degrees.
78 A F B 39
Let O be the center of the incircle
ECOD forms a quadrilateral with angles OEC and OED both being right
So angle EOD = 180 - angle C = 180- 33 = 147° = minor arc ED
And angle EFD is an inscribed angle inrercepting this arc
So its measure = 147 / 2 = 73.5°