Question

which angles are supplementary to each other? select all that apply.
$\angle bfc$ and $\angle cfd$
$\angle efb$ and $\angle dfe$
$\angle cfd$ and $\angle dfe$
$\angle efb$ and $\angle cfd$

Explanation:

Supplementary angles sum to $180^\circ$ (form a straight line).

1. $\angle BFC$ is a right angle ($90^\circ$), $\angle CFD$ is a right angle ($90^\circ$); $90^\circ+90^\circ=180^\circ$, so they are supplementary.
2. $\angle EFB$ spans $\angle BFC + \angle CFE = 90^\circ+\angle CFE$, $\angle DFE$ is adjacent to $\angle CFE$ on a straight line, so $\angle EFB + \angle DFE = 180^\circ$, making them supplementary.
3. $\angle CFD$ is $90^\circ$, $\angle DFE$ is less than $90^\circ$, their sum is less than $180^\circ$, so not supplementary.
4. $\angle EFB$ is greater than $90^\circ$, $\angle CFD$ is $90^\circ$, their sum is greater than $180^\circ$, so not supplementary.

Answer:

• $\angle BFC$ and $\angle CFD$
• $\angle EFB$ and $\angle DFE$