Archie has been working on a proof of the Triangle Angle Sum Theorem. One part of his proof is missing. Which answer choice correctly completes his proof? Archie's Proof: Given the diagram shown, ∠1≅∠5 ; ∠2≅∠4 because alternate interior angles are congruent when lines are parallel. Then, I know that m∠1=m∠5 ; m∠2=m∠4 because congruent angles have equal measures. _________________ by the definition of a straight angle. Finally, m∠1+m∠3+m∠2=180° by substitution. (1 point) Responses m∠2+m∠3+m∠4=180° m angle 2 plus m angle 3 plus m angle 4 equals 180 degrees m∠5+m∠3+m∠4=180° m angle 5 plus m angle 3 plus m angle 4 equals 180 degrees m∠1+m∠3+m∠2=180° m angle 1 plus m angle 3 plus m angle 2 equals 180 degrees m∠5+m∠3+m∠1=180°

Answer 1

To correctly complete Archie's proof of the Triangle Angle Sum Theorem, the missing statement must articulate the relationship between the angles formed when the lines are intersected. Given that ∠1 and ∠2 are supplementary to the angle ∠3, the appropriate choice involves establishing that the sum of two angles and an angle adjacent to those angles amounts to 180 degrees, confirming that they make a straight angle.

The correct choice that completes the proof is:

m∠1+m∠3+m∠2=180° by the definition of a straight angle.