Question

what is a pair of supplementary angles if line m and n are parallel?
○ ∠1 and ∠8
○ ∠5 and ∠8
○ ∠7 and ∠2
○ ∠4 and ∠6

Explanation:

Step1: Define supplementary angles

Supplementary angles sum to $180^\circ$.

Step2: Analyze each option

• $\angle1$ and $\angle8$: Alternate exterior angles, equal ($\angle1=\angle8$), not supplementary unless right angles.
• $\angle5$ and $\angle8$: Linear pair, sum to $180^\circ$, supplementary, but check parallel line rules.
• $\angle7$ and $\angle2$: Alternate exterior angles, equal ($\angle7=\angle2$), not supplementary unless right angles.
• $\angle4$ and $\angle6$: Alternate interior angles, equal ($\angle4=\angle6$), not supplementary unless right angles.

Step3: Confirm valid pair

$\angle5$ and $\angle8$ form a linear pair, so their sum is $180^\circ$.

Answer:

$\boldsymbol{\angle5 \text{ and } \angle8}$