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

Let's fill in the blanks in your proof step by step:

1. Given the diagram shown, \( \angle 1 \cong \angle 5 \); \( \angle 2 \cong \angle 4 \) because alternate interior angles are congruent when lines are parallel.

2. Then, I know that \( m\angle 1 = m\angle 5 \); \( m\angle 2 = m\angle 4 \) because congruent angles have equal measures.

3. \( m\angle 1 + m\angle 3 + m\angle 4 = 180^\circ \) by the definition of a straight angle.

4. Finally, \( m\angle 1 + m\angle 3 + m\angle 2 = 180^\circ \) by substitution.

Thus, the final filled proof is:

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

This completes the proof that \( m\angle 1 + m\angle 3 + m\angle 2 = 180^\circ \).