We are given that ∠1 and ∠2 are complementary angles. This means their sum is 90°. The expressions for their measures are:

$m∠1 = (2x - 26)^\circ$ $m∠2 = (4x - 28)^\circ$

Since they are complementary, we can set up the equation:

$m∠1 + m∠2 = 90^\circ$

Substitute the expressions for $m∠1$ and $m∠2$:

$(2x - 26) + (4x - 28) = 90$

Now, simplify the equation:

$6x - 54 = 90$

Add 54 to both sides:

$6x = 144$

Divide by 6:

$x = 24$

Now, substitute $x = 24$ into the expression for $m∠2$:

$m∠2 = 4x - 28 = 4(24) - 28 = 96 - 28 = 68^\circ$

Thus, the measure of ∠2 is 68°.

Would you like further clarification or details?

Here are some related questions:

1. How can you verify if two angles are complementary?
2. What happens if the sum of two angles is greater than 90°?
3. How do you solve for the value of $x$ in complementary angle problems?
4. What is the relationship between supplementary and complementary angles?
5. How do we classify angles based on their measures?

Tip: In complementary angle problems, always remember their sum equals 90°, which simplifies finding unknowns.