The following is the proof of Triangle Angle Sum Theorem. Which statement has a mistake and how should the mistake be fixed? Given: ΔABC with DE←→∥AC¯¯¯¯¯¯¯¯ Prove: m∠A+m∠ABC+m∠C=180° Statements Reasons 1. ΔABC with DE←→∥AC¯¯¯¯¯¯¯¯ 1. Given 2. ∠DBA≅∠B; ∠EBC≅∠C 2. DE←→∥AC¯¯¯¯¯¯¯¯ and alternate interior angles are congruent when lines are parallel. 3. m∠DBA=m∠A; m∠EBC=m∠C 3. Definition of congruent triangles 4. m∠DBA+m∠ABC+m∠EBC=180° 4. Definition of a straight angle 5. m∠A+m∠ABC+m∠C=180° 5. Substitution (1 point) Responses Statement 4 has a mistake. It should say m∠A+m∠ABC+m∠C=180° . Statement 4 has a mistake. It should say m∠A+m∠ABC+m∠C=180° . Statement 4 has a mistake. It should say m∠DBA+m∠ABC+m∠ACB=180° . Statement 4 has a mistake. It should say m∠DBA+m∠ABC+m∠ACB=180° . Statement 2 has a mistake. It should say ∠DBA≅∠B; ∠EBC≅∠A . Statement 2 has a mistake. It should say ∠DBA≅∠B; ∠EBC≅∠A . Statement 2 has a mistake. It should say ∠DBA=∠A; ∠EBC=∠C .

Answer 1

The statement that contains a mistake is Statement 4.

The reason for this is that Statement 4 claims that \( m\angle DBA + m\angle ABC + m\angle EBC = 180^\circ \), but it should actually refer to the angles of triangle \( ABC \). The correct version of Statement 4 should say:

Statement 4 should say: \( m\angle DBA + m\angle ABC + m\angle ACB = 180^\circ \).

This correction maintains that the sum of angles in any triangle (in this case, triangle \( ABC \)) is indeed \( 180^\circ \), which is the fundamental concept being proven by the Triangle Angle Sum Theorem.

Thus, the specific correction for Statement 4 is to replace \( m\angle EBC \) with \( m\angle ACB \). The other statements remain valid for the proof.