Question

which angles are supplementary to each other?
options: ∠6 and ∠3, ∠4 and ∠3, ∠2 and ∠4, ∠4 and ∠5

Explanation:

Step1: Define supplementary angles

Supplementary angles sum to $180^\circ$.

Step2: Analyze each option

• $\angle6$ and $\angle3$: $\angle3=90^\circ$, $\angle6$ is acute, sum $

eq180^\circ$.

• $\angle4$ and $\angle3$: $\angle3=90^\circ$, $\angle4$ is acute, sum $

eq180^\circ$.

• $\angle2$ and $\angle4$: $\angle2=\angle5$ (vertical angles), $\angle4+\angle5=180^\circ$, so $\angle2+\angle4=180^\circ$.
• $\angle4$ and $\angle5$: They are adjacent acute angles, sum $

eq180^\circ$.

Answer:

$\boldsymbol{\angle2 \text{ and } \angle4}$