Question

which of the following conclusions can be made using the given information?
∠abc and ∠def are supplementary because the definition of supplementary angles is angles whose measure add to 180° and 80° + 100° = 180°.
∠abc and ∠def are not supplementary because they do not look like they would line up to form a straight line.
∠abc and ∠def are supplementary because they look like they would line up to form a straight line.
∠abc and ∠def are not supplementary because they do not meet.

Explanation:

Step1: Recall definition of supplementary angles

Supplementary angles are two angles whose measures sum to 180°.

Step2: Check the sum of given angles

Given $\angle ABC = 100^{\circ}$ and $\angle DEF=80^{\circ}$, and $80^{\circ}+100^{\circ}=180^{\circ}$.

Answer:

$\angle ABC$ and $\angle DEF$ are supplementary because the definition of supplementary angles is angles whose measure add to 180° and $80^{\circ}+100^{\circ}=180^{\circ}$.