Question

two parallel lines, p and q, are cut by the transversal k as shown. suppose m∠1 = 55°. complete the statements below. we see that ∠1 and ∠2 are (choose one) thus, ∠1 and ∠2 are (choose one) so, m∠2 = °. we see that ∠2 and ∠3 are (choose one) and since the lines p and q are parallel, ∠2 and ∠3 are (choose one)

Explanation:

Step1: Identify angle - pair relationship of ∠1 and ∠2

∠1 and ∠2 are vertical angles.

Step2: Recall property of vertical angles

Vertical angles are congruent.

Step3: Determine the measure of ∠2

Since ∠1 and ∠2 are congruent and m∠1 = 55°, m∠2=55°.

Step4: Identify angle - pair relationship of ∠2 and ∠3

∠2 and ∠3 are corresponding angles.

Step5: Recall property of corresponding angles for parallel lines

When two parallel lines are cut by a transversal, corresponding angles are congruent.

Answer:

We see that ∠1 and ∠2 are vertical angles.
Thus, ∠1 and ∠2 are congruent.
So, m∠2 = 55°.
We see that ∠2 and ∠3 are corresponding angles.
And since the lines p and q are parallel, ∠2 and ∠3 are congruent.