Angles. Triangle angles.
The sum of angles of a triangle equals 180°.
Therefore:
|∠EAB| + |∠ABE| + |∠BEA| = 180°
Susbtitute
|∠EAB| = 14°
|∠ABE| = 45°
|∠BEA| = x°
14° + 45° + x° = 180°
59° + x° = 180° |subtract 59° from both sides
x° = 121°
∠BEA and ∠CED are vertical angles. Vertical angles are congruent, meaning that they have the same angle measure.
Therefore
|∠CED| = 121°
In ΔCDE:
|∠CED| + |∠DCE| + |∠EDC| = 180°
Substitute:
|∠CED| =121°
|∠DCE| = 27°
|∠EDC| = y°
121° + 27° + y° = 180°
148° + y° = 180° |subtract 148° from both sides
y° = 32°
|∠EDC| = 32°