Question

which of the angles in the figure are supplementary to ∠3? ∠2 ∠1,∠4,∠5 and ∠8 ∠2,∠7, and ∠6 ∠2 and ∠4

Explanation:

Step1: Recall supplementary - angle definition

Two angles are supplementary if their sum is $180^{\circ}$.

Step2: Analyze linear - pair relationships

$\angle3$ and $\angle1$ form a linear pair, so $\angle3+\angle1 = 180^{\circ}$. Also, $\angle3$ and $\angle4$ are vertical - angle related to $\angle1$ and $\angle3$'s linear - pair relationship. Since vertical angles are equal, and $\angle1$ is supplementary to $\angle3$, $\angle4$ is also supplementary to $\angle3$.

Step3: Consider parallel - line properties

If we assume the lines $m$ and $n$ are parallel (not explicitly stated but a common geometric setup), using the properties of parallel lines cut by a transversal, $\angle3$ and $\angle5$ are same - side interior angles, so $\angle3+\angle5=180^{\circ}$. And $\angle5$ and $\angle8$ are vertical angles, so $\angle8$ is also supplementary to $\angle3$.

Answer:

B. $\angle1,\angle4,\angle5$ and $\angle8$