https://file.aiquickdraw.com/mathbot/file/1726861640480derzt0kw.jpg

**Examine the diagram above and determine the following:**

The angle relationship is         [ Select ]      ["Corresponding Angles", "Alternate Exterior Angles", "Supplementary Angles", "Alternate Interior Angles"] 

The value of x is equal to         [ Select ]      ["10", "6", "7", "5"] 

The measure of the angle in bold is         [ Select ]      ["85°", "105°", "125°", "110°"] 

Let's analyze the diagram step by step to determine the requested information.

### 1. **Identifying the Angle Relationship:**
The angles shown in the diagram are on opposite sides of the transversal, and they are on opposite sides of the parallel lines. This makes them **alternate exterior angles**. Alternate exterior angles are equal when the lines are parallel.

Therefore, the correct relationship is: **Alternate Exterior Angles**.

### 2. **Finding the Value of \( x \):**
Since the angles are alternate exterior angles and are equal, we can set up the following equation:

\[
17x = 18x - 5
\]

Now, solve for \( x \):

\[
17x - 18x = -5
\]
\[
-x = -5
\]
\[
x = 5
\]

Thus, the value of \( x \) is **5**.

### 3. **Calculating the Measure of the Angle:**
Now, substitute \( x = 5 \) into either of the angle expressions to find the measure of the angle. Let's use the expression \( 17x \):

\[
17x = 17 \times 5 = 85^\circ
\]

So, the measure of the angle is **85°**.

### Summary:
- **Angle relationship:** Alternate Exterior Angles
- **Value of \( x \):** 5
- **Measure of the bold angle:** 85°

Would you like any additional details or clarifications on any of these steps?

### Follow-up Questions:
1. What is the difference between alternate exterior and alternate interior angles?
2. Can you explain how to determine if two angles are corresponding?
3. What are supplementary angles, and how do they differ from alternate exterior angles?
4. How would you solve this if the angles were supplementary instead of equal?
5. What happens if the lines are not parallel? How does that affect the angle relationships?

### Tip:
When working with angles formed by parallel lines and a transversal, identifying the type of angle relationship (alternate, corresponding, etc.) is key to solving for unknown variables quickly!

Examine the diagram above and determine the following: The angle relationship is [ Select ] ["Corresponding Angles", "Alternate Exterior Angles", "Supplementary Angles", "Alternate Interior Angles"] The value of x is equal to [ Select ] ["10", "6", "7", "5"] The measure of the angle in bold is [ Select ] ["85°", "105°", "125°", "110°"]

Analyze a diagram showing parallel lines and a transversal, using the alternate exterior angles theorem to find the value of x and the angle measures. This problem is suitable for students in Grades 7-9, covering key algebra and geometry concepts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation