Two angles are considered complementary if their measures add up to $90^\circ$. Given that ∠1 is a complement of ∠2, we have:

$m∠1 + m∠2 = 90^\circ$

Given that $m∠1 = 23^\circ$, we can substitute this into the equation:

$23^\circ + m∠2 = 90^\circ$

Now, solve for $m∠2$:

$m∠2 = 90^\circ - 23^\circ = 67^\circ$

Conclusion:

$m∠2 = 67^\circ$

Would you like more details, or do you have any questions?

Here are 5 related questions for further practice:

1. If ∠3 is a complement of ∠4 and $m∠3 = 45^\circ$, what is $m∠4$?
2. If ∠A is a supplement of ∠B, and $m∠A = 110^\circ$, what is $m∠B$?
3. What is the difference between complementary and supplementary angles?
4. If ∠X and ∠Y are complementary, and $m∠X = (2x + 5)^\circ$ and $m∠Y = (3x - 15)^\circ$, what is the value of $x$?
5. Two angles are complementary, and one angle is four times the other. What are the measures of the two angles?

Tip: Remember that complementary angles always add up to $90^\circ$, while supplementary angles add up to $180^\circ$.