We are given that two angles, $\angle 1$ and $\angle 2$, are complementary. Complementary angles add up to 90°, so we can set up the equation:

$m\angle 1 + m\angle 2 = 90^\circ$

The expressions for the measures of the angles are given as:

$m\angle 1 = 2x - 19$

$m\angle 2 = x + 7$

Now, substitute these expressions into the complementary angle equation:

$(2x - 19) + (x + 7) = 90$

Simplify the equation:

$2x - 19 + x + 7 = 90$

Combine like terms:

$3x - 12 = 90$

Add 12 to both sides:

$3x = 102$

Now, divide both sides by 3:

$x = 34$

Now that we have the value of $x$, we can find the measure of $\angle 2$:

$m\angle 2 = x + 7 = 34 + 7 = 41^\circ$

Thus, the measure of $\angle 2$ is 41°.

Would you like further details or explanations? Here are some follow-up questions:

1. What are complementary angles, and how do they relate to each other?
2. How would you solve a problem with supplementary angles?
3. How do you check if your solution is correct?
4. Can complementary angles have variables like this in other problems?
5. What happens if you solve the equation incorrectly?

Tip: When solving equations with variables, always double-check your work after simplifying to avoid mistakes!