Question

Use the image to answer the question.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

Based on the provided proof structure for demonstrating that the sum of the measures of the exterior angles of a triangle is 360°, here's how you can fill in the blanks in step 2:

1. Consider a triangle with interior angles ∠2, ∠5, and ∠3 and corresponding exterior angles ∠1, ∠4, and ∠6.
   Reason: Given

2. \( m∠1 + m∠2 = 180° \)
   \( m∠4 + m∠5 = 180° \)
   \( m∠6 + m∠3 = 180° \)
   Reason: Definition of Linear Pairs

3. \((m∠1 + m∠2) + (m∠4 + m∠5) + (m∠6 + m∠3) = 180° + 180° + 180° \)
   Reason: Addition

4. \((m∠2 + m∠3 + m∠5) + (m∠1 + m∠4 + m∠6) = 540° \)
   Reason: Rearrange and simplify

5. \(m∠2 + m∠3 + m∠5 = 180° \)
   Reason: Triangle Angle Sum Theorem

6. \(180° + (m∠1 + m∠4 + m∠6) = 540° \)
   Reason: Substitution

7. \((m∠1 + m∠4 + m∠6) = 360° \)
   Reason: Subtraction Property of Equality

This completed proof shows that the exterior angles add up to 360° by utilizing the properties of linear pairs and the triangle angle sum theorem.