Question

in this figure, parallel lines a and b are intersected by line c. which pair of angles is not supplementary? a ∠1 and ∠6 b ∠3 and ∠8 c ∠2 and ∠7 d ∠4 and ∠6

Explanation:

Step1: Recall supplementary - angle definition

Two angles are supplementary if their sum is 180°.

Step2: Analyze option A

∠1 and ∠6 are not supplementary. They are neither a linear - pair nor related in a way that their sum is 180° when a and b are parallel lines intersected by c.

Step3: Analyze option B

∠3 and ∠8 are supplementary. They are same - side exterior angles. When two parallel lines a and b are intersected by a transversal c, same - side exterior angles are supplementary.

Step4: Analyze option C

∠2 and ∠7 are supplementary. They are same - side interior angles. When two parallel lines a and b are intersected by a transversal c, same - side interior angles are supplementary.

Step5: Analyze option D

∠4 and ∠6 are supplementary. They are same - side interior angles. When two parallel lines a and b are intersected by a transversal c, same - side interior angles are supplementary.

Answer:

A. ∠1 and ∠6