Question

The drawn line is parallel to the triangle segment joining the vertices of angles 1 and 2. The line, with arrows at both ends, passes through the vertex of angle 3, forming two more angles. Angle 4 is formed where the drawn line meets the base of the triangle from angle 2 to angle 3. Angle 5 is formed where the drawn line meets the side from angle 1 to 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 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∠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∠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

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