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

- m∠1 = (6x + 18)°
- m∠2 = (3x − 9)°

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

\[
m∠1 + m∠2 = 90°
\]

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

\[
(6x + 18) + (3x − 9) = 90
\]

Now, combine like terms:

\[
6x + 3x + 18 − 9 = 90
\]
\[
9x + 9 = 90
\]

Solve for \(x\):

\[
9x = 90 − 9
\]
\[
9x = 81
\]
\[
x = \frac{81}{9} = 9
\]

Now that we know \(x = 9\), substitute this value back into the expression for m∠1:

\[
m∠1 = 6x + 18 = 6(9) + 18 = 54 + 18 = 72°
\]

Therefore, the measure of ∠1 is **72°**.

Would you like more details or have any questions?

Here are some related questions you might consider:
1. What would happen if the angles were supplementary instead of complementary?
2. How would the solution change if m∠1 were (7x + 10)° and m∠2 were (2x - 5)°?
3. Can two angles both be 45° and still satisfy the given conditions?
4. What if the sum of the angles was 180° instead of 90°?
5. How would you verify the solution by substituting back into both angle equations?

**Tip:** Always double-check the angle sum when working with complementary or supplementary angles to ensure the correct relationship is used.

∠1 and ∠2 are complementary angles. If m∠1 = (6x + 18)° and m∠2 = (3x − 9)°, find the measure of ∠1.

Learn how to solve for the measure of an angle when given two complementary angles in the form of algebraic expressions. This step-by-step solution includes solving for x and calculating the final measure of the angles.

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