Answer:
∠CDE = 14°
Step-by-step explanation:
Since CE is extended to point F then ∠FED is an external angle of the triangle
The external angle of a triangle is equal to the sum of the 2 opposite interior angles, that is
∠FED = ∠ECD + ∠CDE ← substitute values
4x + 5 = x + 8 + x + 9, that is
4x + 5 = 2x + 17 ( subtract 2x from both sides )
2x + 5 = 17 ( subtract 5 from both sides )
2x = 12 ( divide both sides by 2 )
x = 6
Hence
∠CDE = x + 8 = 6 + 8 = 14°
