Prove that the sum of the measures of the exterior angles of the triangle is 360°. Fill in the blanks in step 2 to complete the proof.(1 point)Statement Reason1. Consider a triangle with interior angles ∠2, ∠5, and ∠3 and corresponding exterior angles ∠1, ∠4, and ∠6 1. given2. m∠1+m∠2=180°m∠5+m∠6=180°$$2. Definition of Linear Pairs3. (m∠1+m∠2)+(m∠5+m∠6)+(m∠3+m∠4)=180°+180°+180° 3. addition4. (m∠2+m∠3+m∠5)+(m∠1+m∠4+m∠6)=540° 4. rearrange and simplify5. m∠2+m∠3+m∠5=180° 5. Triangle Angle Sum Theorem6. 180°+(m∠1+m∠4+m∠6)=540° 6. substitution7. (m∠1+m∠4+m∠6)=360° 7. Subtraction Property of Equality

Answer 1

To complete the proof, we need to fill in the blanks appropriately in step 2. Here’s the completed proof with the specific statement and reason filled in:

Statement | Reason --- | ---

1. Consider a triangle with interior angles ∠2, ∠5, and ∠3 and corresponding exterior angles ∠1, ∠4, and ∠6 | 1. Given
2. \( m∠1 + m∠2 = 180° \) and \( m∠5 + m∠6 = 180° \) | 2. Definition of Linear Pairs
3. \( (m∠1 + m∠2) + (m∠5 + m∠6) + (m∠3 + m∠4) = 180° + 180° + 180° \) | 3. Addition
4. \( (m∠2 + m∠3 + m∠5) + (m∠1 + m∠4 + m∠6) = 540° \) | 4. Rearrange and Simplify
5. \( m∠2 + m∠3 + m∠5 = 180° \) | 5. Triangle Angle Sum Theorem
6. \( 180° + (m∠1 + m∠4 + m∠6) = 540° \) | 6. Substitution
7. \( (m∠1 + m∠4 + m∠6) = 360° \) | 7. Subtraction Property of Equality

With the correct statements and reasons, we prove that the sum of the measures of the exterior angles of the triangle is indeed \( 360° \).