To solve for the measures of Angle 1 and Angle 2, we first need to understand that a linear pair of angles are adjacent angles that add up to $180^\circ$.

Given:

• Angle 1 = $5x + 9$
• Angle 2 = $3x - 11$

Since they form a linear pair: $\text{Angle 1} + \text{Angle 2} = 180^\circ$ Substitute the given expressions: $(5x + 9) + (3x - 11) = 180$

Now, combine like terms: $5x + 3x + 9 - 11 = 180$ $8x - 2 = 180$

Next, add 2 to both sides: $8x = 182$

Now, divide both sides by 8: $x = \frac{182}{8} = 22.75$

Now that we have the value of $x$, we can find the measures of the angles.

Angle 1: $5x + 9 = 5(22.75) + 9 = 113.75 + 9 = 122.75^\circ$

Angle 2: $3x - 11 = 3(22.75) - 11 = 68.25 - 11 = 57.25^\circ$

Thus, the measures of the angles are:

• Angle 1: $122.75^\circ$
• Angle 2: $57.25^\circ$

Would you like more details or have any questions?

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Here are 5 related questions to deepen your understanding:

1. What are supplementary angles, and how do they relate to a linear pair?
2. How would the problem change if Angle 1 was equal to $7x + 2$ instead?
3. Can two acute angles form a linear pair? Why or why not?
4. How do linear pairs relate to the properties of parallel lines and a transversal?
5. If the sum of the angles were $200^\circ$ instead, what would that imply?

Tip: Remember, the sum of angles in a linear pair is always $180^\circ$, no matter the individual values of the angles.