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.
1 answer
Sure! Here’s the completed proof with the blanks filled in:
Given the diagram shown, ∠5 ≅ ∠1 ; ∠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∠1 + m∠3 + m∠4 = 180° by the definition of a straight angle. Finally, m∠1 + m∠3 + m∠2 = 180° by substitution.
