Use the image to answer the question. Fill in the blanks to complete the proof that m∠1+m∠3+m∠2=180° given the diagram.(2 points)Given the diagram shown, ∠≅∠5; ∠2≅∠4 because alternate interior angles are congruent when lines are parallel. Then, I know that m∠1=m∠5; m∠2=m∠4 because congruent angles have equal measures. m∠+m∠3+m∠4=180° by the definition of a straight angle. Finally, m∠1+m∠3+m∠=180° by substitution.

Answer 1

To complete the proof that \( m∠1 + m∠3 + m∠2 = 180° \) given the provided statement, we need to fill in the blanks strategically:

1. From the given information, we can fill in the first blank:

   • Fill in the first blank: \( m∠4 \)
   • Thus, the complete statement becomes: \( m∠1 + m∠3 + m∠4 = 180° \) by the definition of a straight angle.

2. Now, we will fill in the last blank:

   • Fill in the last blank: \( m∠2 \)
   • The final statement looks like this: \( m∠1 + m∠3 + m∠2 = 180° \) by substitution.

So the completed proof reads:

Given the diagram shown, \( ∠1 ≅ ∠5; ∠2 ≅ ∠4 \) because alternate interior angles are congruent when lines are parallel. Then, I know that \( m∠1 = m∠5; m∠2 = m∠4 \) because congruent angles have equal measures. \( m∠5 + m∠3 + m∠4 = 180° \) by the definition of a straight angle. Finally, \( m∠1 + m∠3 + m∠2 = 180° \) by substitution.