The missing statement and reasons are;
Statement 5; 14x + 15 = 13x + 20
Reason 2; Vertically opposite angles are equal
Reason 4; Transitive property of equality.
Reason 6; Subtraction Property of Equality.
We are given that;
∠BDA ≅ ∠A
We want to prove that; x = 5
Statement 1; ∠BDA ≅ ∠A
Reason; It is Given
Statement 2; ∠BDA ≅ ∠CDE; The statement means they are congruent and equal.
Reason; Vertically opposite angles are equal
Statement 3; ∠CDE ≅ ∠A; This means ∠CDA is congruent to ∠A.
Reason; Transitive property of congruence.
Statement 4; m∠CDE = m∠A. We saw that ∠BDA ≅ ∠A and ∠BDA ≅ ∠CDE. Thus, by transitive property of equality, we can say that; m∠CDE = m∠A.
Reason; Transitive property of equality.
Statement 5; 14x + 15 = 13x + 20
Reason is; Substitution property of equality
Statement 6; 14x = 13x + 5; In statement 5 above, what was done to get this statement 6 was to subtract 15 from both sides. This is known as subtraction property of equality.
Reason; Subtraction Property of Equality.
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