MATH SOLVE

4 months ago

Q:
# Please Help!! What is the next step in the proof? Choose the most logical approach.A. Statement: ∠1 ≅ ∠8 and ∠2 ≅ ∠7Reason: Congruent Supplements TheoremB. Statement: m∠3 + m∠4 = 180° and m∠7 + m∠8 = 180°Reason: Linear Pair TheoremC. Statement: m∠3 + m∠5 = 180° and m∠4 + m∠6 = 180°Reason: definition of supplementary anglesD. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5Reason: Vertical Angles Theorem

Accepted Solution

A:

Answer:statement D is correct.Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5Reason: Vertical Angles TheoremStep-by-step explanation:Given that 3 ≅ ∠7 and ∠4 ≅ ∠8from statement 2 because they are corresponding angles. ∠8 ≅ ∠5 because its vertical anglesThe vertical angles theorem is about angles that are opposite each other. So, ∠4 ≅ ∠8 and ∠8 ≅ ∠5 which means ∠4 ≅ ∠5 Hence,∠3 = ∠7∠4 = ∠5 they are known as interior alternative angles.