Question

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

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 forming a linear - pair. So, $m\angle3 + m\angle4=180^{\circ}$, which means $\angle3$ is supplementary to $\angle4$.

Step3: Analyze vertical - angle relationship

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

Answer:

B. $\angle3$ and $\angle1$