Complementary angles add up to 90°. Given:

$m∠1 = (6x - 15)°$

$m∠2 = (5x + 6)°$

Since they are complementary:

$(6x - 15) + (5x + 6) = 90$

Step 1: Solve for $x$

$6x - 15 + 5x + 6 = 90$

$11x - 9 = 90$

$11x = 99$

$x = 9$

Step 2: Find $m∠1$

$m∠1 = 6(9) - 15$

$= 54 - 15$

$= 39°$

Thus, the measure of ∠1 is 39°.

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Would you like further explanation or another example?

Here are some related questions:

1. What is the measure of ∠2?
2. How do we determine if two angles are complementary?
3. What is the difference between complementary and supplementary angles?
4. Can an angle be both complementary and supplementary?
5. What happens if we change the expressions for ∠1 and ∠2?

Tip:

Complementary angles always sum to 90°, while supplementary angles sum to 180°.