Question

which of the angles in the figure are supplementary to ∠3?
o ∠2
o ∠2,∠7, and ∠6
o ∠1,∠4,∠5 and ∠8
o ∠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 $\angle4$ form a linear pair, so $\angle3+\angle4 = 180^{\circ}$. Also, $\angle3$ and $\angle1$ form a linear pair, so $\angle3+\angle1=180^{\circ}$.

Step3: Use vertical - angle and parallel - line properties

Since vertical angles are equal ($\angle1=\angle5$ and $\angle4 = \angle8$ because of the parallel lines $m$ and $n$ intersected by a transversal), $\angle3+\angle5 = 180^{\circ}$ and $\angle3+\angle8=180^{\circ}$. So $\angle1,\angle4,\angle5$ and $\angle8$ are supplementary to $\angle3$.

Answer:

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