Question

which angles are supplementary to each other?
∠3 and ∠2 ∠6 and ∠3 ∠1 and ∠6 ∠1 and ∠4

Explanation:

Step1: Define supplementary angles

Supplementary angles sum to $180^\circ$.

Step2: Analyze each option

• $\angle3$ and $\angle2$: These are adjacent small angles, sum is less than $180^\circ$.
• $\angle6$ and $\angle3$: $\angle6$ is acute, $\angle3$ is acute, sum is less than $180^\circ$.
• $\angle1$ and $\angle6$: $\angle1$ is a right angle ($90^\circ$), $\angle6$ is acute, sum is less than $180^\circ$.
• $\angle1$ and $\angle4$: $\angle1=90^\circ$, $\angle4=90^\circ$, so $\angle1+\angle4=90^\circ+90^\circ=180^\circ$.

Answer:

$\boldsymbol{\angle1 \text{ and } \angle4}$