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 m∠DCE = 58°
 m∠CDE = 74°
 m∠DAE = 119°
Step-by-step explanation:
The incenter is the point of intersection of the angle bisectors. The angles on either side of the bisector have the same measure. Of course, the sum of angles in a triangle is 180°.
 m∠DCE = 2×29° = 58°
 m∠CDE = 180° -58° -2×24° = 74°
 m∠DAE = 180° -74°/2 -24° = 119°