The problem states that ∠1 and ∠2 are complementary angles, meaning their measures sum to 90°. We are given:

• m∠1 = (2x - 26)°
• m∠2 = (4x - 28)°

Since complementary angles add up to 90°, we can set up the equation:

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

Now, let's solve for $x$ and then substitute the value of $x$ into the expression for m∠2 to find its measure. I'll solve this step by step.

Solving the equation:

$(2x - 26) + (4x - 28) = 90$ Combine like terms: $6x - 54 = 90$ Add 54 to both sides: $6x = 144$ Divide both sides by 6: $x = 24$

Finding the measure of ∠2:

Substitute $x = 24$ into the expression for m∠2: $m∠2 = 4x - 28 = 4(24) - 28 = 96 - 28 = 68°$

Thus, the measure of ∠2 is $\boxed{68^\circ}$.

Would you like further details or have any other questions?

Related Questions:

1. What is the measure of ∠1 for this problem?
2. How do complementary angles differ from supplementary angles?
3. Can you find the value of x if the angles were supplementary instead of complementary?
4. What are the properties of angles formed by parallel lines and transversals?
5. How would the equation change if the angles were congruent instead of complementary?

Tip:

Remember that complementary angles always add up to 90°, while supplementary angles add up to 180°. This distinction is crucial in solving angle-related problems!