Question

Use the image to answer the question.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 Reason1. Consider a triangle with interior angles ∠2, ∠4, and ∠6 and corresponding exterior angles ∠1, ∠3, and ∠5. 1. given2. m∠1+m∠2=180°m∠5+m∠6=180°m∠3+m∠4=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∠4+m∠6)+(m∠1+m∠3+m∠5)=540° 4. rearrange and simplify5. m∠2+m∠4+m∠6=180° 5. Triangle Angle Sum Theorem6. 180°+(m∠1+m∠3+m∠5)=540° 6. substitution7. $$ 7. Subtraction Property of Equality

Answer 1

To complete the proof of the sum of the measures of the exterior angles of a triangle, we need to fill in step 7 appropriately. Here is the completed proof with the appropriate reasoning for step 7:

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. m∠1+m∠3+m∠5=360°
   7. Subtraction Property of Equality

In step 7, we used the Subtraction Property of Equality to subtract 180° from both sides of the equation, leading to the conclusion that the sum of the measures of the exterior angles (m∠1 + m∠3 + m∠5) equals 360°.