Anna wants to prove the Triangle Angle Sum Theorem. What would be the remaining steps to complete her proof? Anna's proof: Step 1: The diagram shows that ∠1≅∠5 and ∠2≅∠4 because alternate interior angles are congruent in parallel lines. Step 2: Then, m∠1≅m∠5 and m∠2≅m∠4 because congruent angles have equal angle measures. (1 point) Responses Step 3: m∠5+m∠3+m∠4=180° by definition of a straight angle. Step 4: m∠1+m∠3+m∠2=180° by substitution. Step 3: m angle 5 plus m angle 3 plus m angle 4 is equal to 180 degrees by definition of a straight angle. Step 4: m angle 1 plus m angle 3 plus m angle 2 is equal to 180 degrees by substitution. Step 3: m∠1+m∠3+m∠2=180° by definition of a straight angle. Step 4: m∠5+m∠3+m∠4=180° by substitution. Step 3: m angle 1 plus m angle 3 plus m angle 2 is equal to 180 degrees by definition of a straight angle. Step 4: m angle 5 plus m angle 3 plus m angle 4 is equal to 180 degrees by substitution. Step 3: m∠5+m∠3+m∠4=180° by definition of a straight angle. Step 4: m∠1+m∠3+m∠2=180° by Triangle Angle Sum theorem. Step 3: m angle 5 plus m angle 3 plus m angle 4 is equal to 180 degrees by definition of a straight angle. Step 4: m angle 1 plus m angle 3 plus m angle 2 is equal to 180 degrees by Triangle Angle Sum theorem. Step 3: m∠2+m∠3+m∠4=180° by definition of a straight angle. Step 4: m∠1+m∠3+m∠2=180° by substitution.

Answer 1

To complete Anna's proof of the Triangle Angle Sum Theorem, after establishing the relationships between the angles, the remaining steps should clearly outline the logical progression from the relationships derived in previous steps to the conclusion that the sum of the angles in a triangle is 180°.

Here are the steps to complete the proof:

Step 3: Since \(m∠5 + m∠3 + m∠4 = 180°\) (by definition of a straight angle), we can substitute the measures of angles that are congruent to \(∠5\) and \(∠4\) based on the earlier established congruences.

Step 4: Substituting \(m∠1\) for \(m∠5\) and \(m∠2\) for \(m∠4\) yields \(m∠1 + m∠3 + m∠2 = 180°\).

Conclusion: Therefore, we have proven that the sum of the angles in triangle \(ABC\) (where angles \(A\), \(B\), and \(C\) correspond to \(∠1\), \(∠2\), and \(∠3\)) is \(180°\) by the Triangle Angle Sum Theorem.

By following these steps, Anna provides a logical and clear conclusion to her proof.