The missing statement is S5: m∠CDE = 11x + 23°. This follows from the given information and the properties of congruent angles and corresponding angles. By solving the resulting equation, we get x = 3.
Missing statement and reasons for the proof:
The missing statement is S5: (m\angle CDE = 11x + 23°).
Here's the reasoning for each step:
S1 and R1: Given that ∠BDA ≅ ∠A.
S2 and R2: Since vertical angles are congruent, we have ∠BDA ≅ ∠CDE.
S3 and R3: Using the transitive property of congruence, if ∠BDA ≅ ∠A and ∠BDA ≅ ∠CDE, then ∠A ≅ ∠CDE.
S4 and R4: Because corresponding angles of congruent triangles are congruent, ∠A ≅ ∠CDE implies that their measures are equal, i.e., m∠A = m∠CDE.
S5: Substitute the value of m∠A from the given information, as mentioned above.
S6 and R6: Subtract 11x from both sides of the equation in S5 to isolate x.
S7 and R7: Finally, simplify the expression to obtain x = 3.