Question

if l || m, identify the angle pair as congruent or supplementary. justify your reasoning by classifying the angle pair.

1. ∠1 and ∠8
2. ∠5 and ∠6
3. ∠6 and ∠8
4. ∠2 and ∠3
5. ∠4 and ∠7
6. ∠3 and ∠6

Explanation:

Step1: Recall angle - pair definitions

Congruent angles have equal measures. Supplementary angles add up to 180 degrees.

Step2: Analyze ∠1 and ∠8

They are vertical angles. Vertical angles are congruent. So, ∠1 and ∠8 are congruent.

Step3: Analyze ∠5 and ∠6

They are adjacent angles that form a straight - line. So, ∠5+∠6 = 180 degrees, and they are supplementary.

Step4: Analyze ∠6 and ∠8

They are neither vertical angles nor do they add up to 180 degrees. They are non - congruent and non - supplementary.

Step5: Analyze ∠2 and ∠3

They are adjacent angles that form a straight - line. So, ∠2+∠3 = 180 degrees, and they are supplementary.

Step6: Analyze ∠4 and ∠7

They are vertical angles. Vertical angles are congruent. So, ∠4 and ∠7 are congruent.

Step7: Analyze ∠3 and ∠6

They are non - adjacent angles and do not have a sum of 180 degrees or equal measures. They are non - congruent and non - supplementary.

Answer:

Angle Pair	Congruent or Supplementary?	Classify
∠5 and ∠6	Supplementary	Linear pair
∠6 and ∠8	Neither
∠2 and ∠3	Supplementary	Linear pair
∠4 and ∠7	Congruent	Vertical angles
∠3 and ∠6	Neither