Answer:
See below, where we have used the definitions of vertical angles and complementary angles, and used the substitution property of equality.
Explanation:
You want a proof that angles complementary to congruent angles are congruent. That is, ∠1 ≅ ∠4.
Statement . . . . Reason
1. ∠1 and ∠3 are complementary . . . . given
2. ∠2 and ∠4 are complementary . . . . given
3. ∠2 ≅ ∠3 . . . . vertical angles are congruent
4. ∠1 +∠3 = 90° . . . . definition of complementary
5. ∠2 +∠4 = 90° . . . . definition of complementary
6. ∠1 +∠3 = ∠2 +∠4 . . . . substitution property of equality
7. ∠1 +∠2 = ∠2 +∠4 . . . . substitution property of equality
8. ∠1 = ∠4 . . . . subtraction property of equality
9. ∠1 ≅ ∠4 . . . . definition of angle congruence
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Additional comment
The idea of congruence applies to the shape of the geometry. The idea of equality applies to the measures of the angles. Angles are congruent when they have the same measure.