Question

HELPPP Provide the missing statements and reasons for the following proof:

Answer 1

The missing statements and reasons in the proof showing that ∠1 is supplementary to ∠2 are:

S2: ∠2 ≅ ∠3

R2: corresponding angles

S3: m∠2 ≅ m∠3

R3: Definition of congruent angles

R5: Definition of supplementary angles

S7: m∠1 + m∠2 = 180°

S8: ∠1 is supplementary to ∠2

Given the proof to show that ∠1 is supplementary to ∠2, thus:

Since lines m and n are parallel to each other,

∠2 and ∠3 are corresponding angles, so, ∠2 ≅ ∠3 based on the corresponding angles theorem.

Since ∠1 and ∠3 form a linear pair, they are supplementary to each other.

By substitution, we would have m∠1 + m∠2 = 180°.

Therefore, we can conclude that ∠1 is supplementary to ∠2.

In summary, the missing statements and reasons in the proof showing that ∠1 is supplementary to ∠2 are:

S2: ∠2 ≅ ∠3

R2: corresponding angles

S3: m∠2 ≅ m∠3

R3: Definition of congruent angles

R5: Definition of supplementary angles

S7: m∠1 + m∠2 = 180°

S8: ∠1 is supplementary to ∠2

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