If angles $\angle ABC$ and $\angle DEF$ are supplementary, this means their measures add up to $180^\circ$.

You are given that:

$m\angle ABC = 92^\circ$

To find $m\angle DEF$, use the relationship between supplementary angles:

$m\angle ABC + m\angle DEF = 180^\circ$

Substitute the given value of $m\angle ABC$:

$92^\circ + m\angle DEF = 180^\circ$

Now, solve for $m\angle DEF$:

$m\angle DEF = 180^\circ - 92^\circ = 88^\circ$

Therefore, $m\angle DEF = 88^\circ$.

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Do you need more details on supplementary angles or any other concepts? Here are some related questions you might find helpful:

1. What are the properties of supplementary angles?
2. How do complementary angles differ from supplementary angles?
3. Can two obtuse angles be supplementary?
4. What happens if both angles are right angles?
5. How do adjacent and non-adjacent supplementary angles differ?

Tip: Always remember that supplementary angles sum up to $180^\circ$, while complementary angles sum to $90^\circ$.