Final answer:
The reason for statement 7 in a two-column proof when given that angles a and b are supplementary and angle a is 90°, is to conclude that angle a and angle b must both be 90° to satisfy the supplementary condition, proving angle a is congruent to angle b.
Step-by-step explanation:
The reason for statement 7 in a two-column proof asserting that ∠a ≅ ∠b given that ∠a and ∠b are supplementary and m∠a=90°, is to show that both angles are equal, which would lead to proving ∠a ≅ ∠b. Since the angles are supplementary, their measures add up to 180°. Having m∠a as 90° would imply that m∠b must also be 90° to satisfy the definition of supplementary angles (90° + 90° = 180°), thus ∠a ≅ ∠b because they both have the same measure.