The problem states that ∠1 and ∠2 are complementary angles. Therefore, their measures add up to 90 degrees. We are given:

• m∠1 = (2x - 13)°
• m∠2 = (2x + 7)°

Since ∠1 and ∠2 are complementary, we know:

$m∠1 + m∠2 = 90°$

Substituting the expressions for m∠1 and m∠2:

$(2x - 13) + (2x + 7) = 90$

Now, let's solve for $x$:

$2x - 13 + 2x + 7 = 90$ $4x - 6 = 90$ $4x = 96$ $x = 24$

Now that we know $x = 24$, we can substitute it back into the expression for m∠1 to find the measure of ∠1:

$m∠1 = 2(24) - 13 = 48 - 13 = 35°$

Thus, the measure of ∠1 is 35 degrees.

Would you like any further details or explanations?

5 Related Questions:

1. How do you calculate the measure of complementary angles?
2. What happens if two angles are supplementary instead of complementary?
3. Can you provide more examples involving complementary angles?
4. How would you solve this if the angles were given in terms of different variables?
5. What is the relationship between linear pairs of angles?

Tip:

When solving problems involving complementary or supplementary angles, always start by setting up the equation that reflects their sum (90° for complementary and 180° for supplementary).