Question

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∠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°
 
  m angle 5 plus m angle 3 plus m angle 1 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∠2+m∠3+m∠4=180°
 
  m angle 2 plus m angle 3 plus m angle 4 equals 180 degrees  
Remaining

Answer 1

To complete Archie's proof of the Triangle Angle Sum Theorem, we need to find the statement that correctly follows from the fact that the angles are arranged in a way such that one of them, along with two others, form a straight angle.

Given that ∠1 and ∠5 are congruent and that ∠2 and ∠4 are also congruent, we know that ∠1, ∠2, and ∠3 together form a straight angle (since they are adjacent angles on a straight line, assuming this setup involves a triangle).

The correct completion of the proof would be:

**m∠5 + m∠3 + m∠4 = 180°**

This follows because angles ∠5 and ∠4 are related through their congruence with ∠1 and ∠2, respectively, and together with ∠3, they form a straight angle.

Thus, the complete statement would be that these three angles sum up to form a straight angle, which is defined as 180 degrees. Thus, the answer choice:

**m∠5 + m∠3 + m∠4 = 180°**
is correct and appropriately completes Archie's proof.