angle 1 and angle 2 form a linear pair. if angle 1 = 5x+9 and angle 2 = 3x-11 find the measure of each angle

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.

Learn how to solve a problem involving angles forming a linear pair, where Angle 1 = 5x + 9 and Angle 2 = 3x - 11. Understand the concept of linear pairs and how to find the measures of angles using algebraic expressions. Suitable for Grades 7-9.

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