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?

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.