Question

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

Explanation:

Step1: Recall supplementary - angle definition

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

Step2: Analyze adjacent angles

$\angle3$ and $\angle4$ are adjacent angles that form a straight - line. So, $\angle3+\angle4 = 180^{\circ}$, which means $\angle3$ is supplementary to $\angle4$.

Step3: Analyze vertical - angle relationship

$\angle1$ and $\angle3$ are vertical angles, so $\angle1=\angle3$. Since $\angle3+\angle4 = 180^{\circ}$, then $\angle1+\angle4 = 180^{\circ}$, and $\angle1$ is also supplementary to $\angle4$.

Answer:

B. $\angle3$ and $\angle1$