Prove that the sum of the measures of the exterior angles of the triangle is 360º. Fill in the blanks in step 7 to complete the proof. (1 point) Statement Reason 1. Consider a triangle with interior angles ∠2, ∠4 , and ∠6 and corresponding exterior angles ∠1, ∠3 , and ∠5 . 1. given 2. m∠1+m∠2=180° m∠5+m∠6=180° m∠3+m∠4=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∠4+m∠6)+(m∠1+m∠3+m∠5)=540° 4. rearrange and simplify 5. m∠2+m∠4+m∠6=180° 5. Triangle Angle Sum Theorem 6. 180°+(m∠1+m∠3+m∠5)=540° 6. substitution 7. $$ 7. Subtraction Property of Equality

Answer 1

To complete step 7 of your proof, we will subtract the sum of the interior angles from the total sum calculated in step 6. Here's how it looks:

Completed Proof:

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

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

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

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

5. \( m∠2 + m∠4 + m∠6 = 180° \)
   Reason: Triangle Angle Sum Theorem

6. \( 180° + (m∠1 + m∠3 + m∠5) = 540° \)
   Reason: substitution

7. \( m∠1 + m∠3 + m∠5 = 360° \)
   Reason: Subtraction Property of Equality

So, the final statement is that the sum of the measures of the exterior angles of a triangle \( m∠1 + m∠3 + m∠5 = 360° \).