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

Explanation:

Step1: Identify alternate - interior angles

$\angle1\cong\angle5,\angle2\cong\angle4$ (alternate - interior angles of parallel lines)

Step2: Use angle - measure equality of congruent angles

Since $\angle1\cong\angle5$, then $m\angle1 = m\angle5$; since $\angle2\cong\angle4$, then $m\angle2 = m\angle4$

Step3: Consider straight - angle property

$m\angle5+m\angle3 + m\angle4=180^{\circ}$ (a straight - angle measures $180^{\circ}$)

Step4: Substitute equal - measure angles

Substitute $m\angle1$ for $m\angle5$ and $m\angle2$ for $m\angle4$ to get $m\angle1 + m\angle3+m\angle2 = 180^{\circ}$

Answer:

The blanks should be filled with $1$, $5$, $2$ in order.