Question

given ∠1 is a complement of ∠2. ∠2 = ∠3. prove ∠1 is a complement of ∠3. statements reasons 1. ∠1 is a complement of ∠2 1. given 2. ∠2 = ∠3 2. __ 3. m∠1 + m∠2 = 90° 3. 4. m∠2 = m∠3 4. definition of congruent angles 5. 5. substitution property of equality 6. ∠1 is a complement of ∠3. 6. __

Explanation:

Step1: State given congruence

Given

Step2: State complement - angle relationship

Definition of complementary angles (If two angles are complementary, the sum of their measures is 90°)

Step3: Substitute angle measure

$m\angle1 + m\angle3=90^{\circ}$

Step4: Define complementary angles

Definition of complementary angles (If the sum of the measures of two angles is 90°, the angles are complementary)

Answer:

1. Given; 3. Definition of complementary angles; 5. $m\angle1 + m\angle3 = 90^{\circ}$; 6. Definition of complementary angles