Question

FIFTY POINTS! ASAP! DUE IN A FEW MINUTES! Just fill in the blanks!!

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Provide reasons for the proof.

Given: ∠2 ≅ ∠4

and ∠2 and ∠3 are supplementary

Prove: ∠1 ≅ ∠3

Answer 1

For the future students who need answer to this problem ....

Step-by-step explanation:

5. given

7. Transitive property of equality

8. Substitution Property

9. Subtraction Property of Equality

10. Converse of Angles Congruent Postulate

I am writing this test now and these are the answers I put in. It hasn't been graded yet but I'm pretty sure that they are correct. But pls lmk if anything is wrong. HOPE THIS HELPS

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Answer 2

This proof involves the definitions of congruence and supplementary angles, as well as some of the properties of equality.

∠1 and ∠2 are supplementary // given

∠3 and ∠4 are supplementary // given

∠1 ≅ ∠3 // given

m∠1 + m∠2 = 180° // definition of supplementary angles

m∠3 + m∠4 = 180° // definition of supplementary angles

m∠1 + m∠2 = m∠3 + m∠4 // transitive property of equality

m∠1 = m∠3 // definition of congruent angles

m∠1 + m∠2 = m∠1 + m∠4 // substitution property of equality (replaced m∠3 with m∠1)

m∠2 = m∠4 // subtraction property of equality (subtracted m∠1 from both sides)

∠2 ≅ ∠4 // definition of congruent angles

hope this helps

Explanation: