https://file.aiquickdraw.com/mathbot/file/1726774987560x7qkt5ve.jpg

Examine the diagram above and determine the following:

The angle relationship is

The value of x is equal to

The measure of the angle in bold is

In this diagram, we can see that two parallel lines are intersected by a transversal. Based on this, we can solve the problem step by step:

### 1. **Angle Relationship:**
The two angles shown are **corresponding angles** because they are on the same side of the transversal and occupy corresponding positions on the parallel lines. Corresponding angles are always congruent, meaning they have the same measure.

### 2. **Equation Setup:**
Since corresponding angles are congruent, we can set the two expressions for the angles equal to each other:
\[
1 + 8x = 7x + 11
\]

### 3. **Solving for \( x \):**
Now, let's solve the equation:
\[
1 + 8x = 7x + 11
\]
Subtract \( 7x \) from both sides:
\[
1 + x = 11
\]
Subtract 1 from both sides:
\[
x = 10
\]

### 4. **Measure of the Angle in Bold:**
Now that we have \( x = 10 \), we can substitute this value into the expression for the angle in bold (the second angle, \( 7x + 11 \)):
\[
7(10) + 11 = 70 + 11 = 81^\circ
\]

### Final Answers:
1. The angle relationship is **corresponding angles**.
2. The value of \( x \) is **10**.
3. The measure of the angle in bold is **81 degrees**.

Would you like any further clarification or details?

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Here are 5 related questions:
1. How do we determine whether two lines are parallel using angles?
2. What are alternate interior angles, and how do they differ from corresponding angles?
3. Can corresponding angles ever be supplementary? Under what conditions?
4. How would you solve for \( x \) if the angles were supplementary instead of congruent?
5. If the transversal intersects two non-parallel lines, do corresponding angles still have the same relationship?

**Tip:** When two lines are cut by a transversal, always check if the lines are parallel to apply angle relationships like corresponding, alternate interior, or alternate exterior.

Examine the diagram above and determine the following: The angle relationship, the value of x, and the measure of the angle in bold.

Learn how to solve for x and determine the measure of an angle formed by two parallel lines cut by a transversal. This problem covers key geometric concepts, including corresponding angles and simple algebra.

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