Question

which angles are supplementary to each other?
∠4 and ∠2 ∠8 and ∠5 ∠2 and ∠5 ∠1 and ∠8

Explanation:

Step1: Define supplementary angles

Supplementary angles sum to $180^\circ$.

Step2: Analyze each option

• $\angle4$ and $\angle2$: Vertical angles, equal, not supplementary.
• $\angle8$ and $\angle5$: Vertical angles, equal, not supplementary.
• $\angle2$ and $\angle5$: $\angle2 = \angle1$ (vertical angles), $\angle1$ and $\angle5$ are same-side exterior angles, which sum to $180^\circ$. Thus $\angle2 + \angle5 = 180^\circ$.
• $\angle1$ and $\angle8$: Alternate exterior angles, equal, not supplementary.

Answer:

$\boldsymbol{\angle2 \text{ and } \angle5}$