Match the reasons with the statements to complete the proof for theorem 3-6, subtraction property of equality, given that angles 2,3 and angles 1,3 are complementary. given: ∠2 and ∠3 are complementary∠1 and ∠3 are complementaryprove: m∠1 = m∠21.given2.substitution3.m∠1 + m∠3 = m∠2 + m∠3definition of complementary angles4.m∠1 = m∠2subtraction property of equality

1. Angles 2, 3 and angles 1,3 are complementary angles(Given)

2. To prove :

Since Angles 2, 3 and angles 1,3 are complementary.

When angles are complementary, then the sum of the measures of angles is 90 degrees.

So, and (Definition of Complementary angles)

3. (Substitution)

4. (Subtraction property of equality)

Refer the below solution for better understanding.

Step-by-step explanation:

Given :

and are complementary angles.

To Prove :

Given that and are complementary angles and if angles are complementary than sum of the measure of angles theire is .

Therefore, and because they are complimentary angles.

 due to Substitution

due to subtraction property of equality.

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