Question

in the figure shown, line r is parallel to line s. use angle relationships to form an argument that shows that the sum of the interior angles in a triangle is 180°. use the drop - down menus to complete the steps of the argument. step 1: m∠4 + m∠1 + m∠choose... = 180° because these angles form a straight line. step 2: m∠4 = m∠2 because these are choose... angles. step 3: m∠5 = m∠choose... because these are choose... angles. step 4: by substituting congruent angles from steps 2 and 3 into the equation in step 1, the conclusion is m∠2 + m∠1 + m∠3 = choose...

Explanation:

Step1: Identify angle - straight - line relationship

$m\angle4 + m\angle1 + m\angle5=180^{\circ}$ because these angles form a straight line.

Step2: Identify alternate - interior angles

$m\angle4 = m\angle2$ because these are alternate - interior angles (lines $r$ and $s$ are parallel).

Step3: Identify alternate - interior angles

$m\angle5 = m\angle3$ because these are alternate - interior angles (lines $r$ and $s$ are parallel).

Step4: Substitute congruent angles

By substituting congruent angles from Steps 2 and 3 into the equation in Step 1, the conclusion is $m\angle2 + m\angle1 + m\angle3 = 180^{\circ}$.

Answer:

Step 1: $\angle5$; Step 2: alternate - interior; Step 3: $\angle3$, alternate - interior; Step 4: $180^{\circ}$