Question

Use the image to answer the question.

An illustration shows a triangle with angles marked as 1, 2 and 3, clockwise beginning at the top angle. A line is drawn outside of the triangle, passing through the vertex with angle 3.

Sylvie has started a proof of the Triangle Angle Sum Theorem. Which answer choice correctly completes her proof?

Sylvie'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.

(1 point)
Responses

m∠5+m∠3+m∠4=180° by the definition of a straight angle. Finally, m∠1+m∠3+m∠2=180° by the Triangle Angle Sum Theorem.
m angle 5 plus m angle 3 plus m angle 4 equals 180 degrees by the definition of a straight angle. Finally, m angle 1 plus m angle 3 plus m angle 2 equals 180 degrees by the Triangle Angle Sum Theorem.

m∠5+m∠3+m∠4=180° by the definition of a straight angle. Finally, m∠1+m∠3+m∠2=180° by substitution.
m angle 5 plus m angle 3 plus m angle 4 equals 180 degrees by the definition of a straight angle. Finally, m angle 1 plus m angle 3 plus m angle 2 equals 180 degrees by substitution.

m∠1+m∠3+m∠2=180° by the definition of a straight angle. Finally, m∠5+m∠3+m∠4=180° by substitution.
m angle 1 plus m angle 3 plus m angle 2 equals 180 degrees by the definition of a straight angle. Finally, m angle 5 plus m angle 3 plus m angle 4 equals 180 degrees by substitution.

m∠2+m∠3+m∠4=180° by the definition of a straight angle. Finally, m∠1+m∠3+m∠2=180° by substitution.

Answer 1

The correct completion of Sylvie's proof is:

**m∠5+m∠3+m∠4=180° by the definition of a straight angle. Finally, m∠1+m∠3+m∠2=180° by the Triangle Angle Sum Theorem.**

This option appropriately follows from Sylvie’s earlier statements about congruent angles and correctly applies the concept of straight angles along with the Triangle Angle Sum Theorem.