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The problem you're working on involves complementary angles. Let's break it down step by step.

Given:
- \( \angle 1 \) and \( \angle 2 \) are complementary, meaning their measures add up to \( 90^\circ \).
- \( m\angle 1 = 5x - 11 \)
- \( m\angle 2 = 6x + 2 \)

We know that:
\[
m\angle 1 + m\angle 2 = 90^\circ
\]
Substitute the expressions for \( m\angle 1 \) and \( m\angle 2 \):
\[
(5x - 11) + (6x + 2) = 90
\]
Simplify the equation:
\[
5x - 11 + 6x + 2 = 90
\]
\[
11x - 9 = 90
\]
Now, solve for \( x \):
\[
11x = 90 + 9
\]
\[
11x = 99
\]
\[
x = 9
\]

Now that we know \( x = 9 \), substitute it back into the expression for \( m\angle 1 \):
\[
m\angle 1 = 5x - 11 = 5(9) - 11 = 45 - 11 = 34^\circ
\]

Thus, the measure of \( \angle 1 \) is \( 34^\circ \).

Would you like more details or have any other questions?

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Here are 5 related questions for further exploration:
1. What are supplementary angles, and how do they differ from complementary angles?
2. How can you determine the measure of \( \angle 2 \) from the given information?
3. If two angles are supplementary, and one is \( 4x - 15 \), how would you find \( x \)?
4. What is the general method for solving equations involving angles?
5. How do you determine if two angles form a linear pair?

**Tip**: Always double-check your equations after substitution to avoid mistakes in algebraic manipulations.

∠1 and ∠2 are complementary angles. If m∠1 = (5x - 11)° and m∠2 = (6x + 2)°, then find the measure of ∠1.

Learn how to solve complementary angles with linear equations. This problem asks for the measure of ∠1, where ∠1 = (5x - 11)° and ∠2 = (6x + 2)°. Step-by-step algebraic manipulation is used to solve for x and the angle measure. Suitable for Grades 7-9.

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