Question

given the following picture where m and n are parallel and s and t are parallel, determine whether the following angle pairs are congruent or supplementary.
<7 and <11
supplementary
<13 and <12
congruent
<5 and <13
<6 and <3

Explanation:

Step1: Analyze ∠7 and ∠11

Since \(m\parallel n\) and \(s\parallel t\), ∠7 and ∠11 are corresponding angles. Corresponding angles are congruent.

Step2: Analyze ∠13 and ∠12

∠13 and ∠12 are alternate exterior and interior angles. When two parallel lines \(m\parallel n\) and \(s\parallel t\), they are congruent.

Step3: Analyze ∠5 and ∠13

∠5 and ∠13 are vertical angles. Vertical angles are congruent.

Step4: Analyze ∠6 and ∠3

∠6 and ∠3 are same - side interior angles. When two parallel lines \(m\parallel n\) and \(s\parallel t\), same - side interior angles are supplementary.

Answer:

∠7 and ∠11: congruent
∠13 and ∠12: congruent
∠5 and ∠13: congruent
∠6 and ∠3: supplementary