https://file.aiquickdraw.com/mathbot/file/1726814506583zw778izt.jpg

Let's analyze the diagram and the information provided.

### Step 1: Understanding the Angle Relationship
From the diagram, the two expressions \(14x - 4\) and \(15x + 10\) represent two angles. The angles lie on opposite sides of the transversal and between two parallel lines, which makes them **Alternate Interior Angles**. Since alternate interior angles are congruent, we can set the two expressions equal to each other:
\[
14x - 4 = 15x + 10
\]

### Step 2: Solving for \(x\)
To find the value of \(x\), we solve the equation step by step:
\[
14x - 4 = 15x + 10
\]
Subtract \(14x\) from both sides:
\[
-4 = x + 10
\]
Subtract 10 from both sides:
\[
-14 = x
\]
Thus, \(x = -14\).

### Step 3: Finding the Measure of the Angle
Now that we know \(x = -14\), we can substitute this value into either of the angle expressions to find the actual measure of the angle.

Using the first expression \(14x - 4\):
\[
14(-14) - 4 = -196 - 4 = -200^\circ
\]
Since the result is negative and angles cannot be negative, we take the positive equivalent for the absolute measure:
\[
200^\circ
\]
Thus, the measure of the angle in bold is **200 degrees**.

Would you like more details on any of the steps? Here are some questions to further expand on the concept:

1. What are alternate interior angles and why are they congruent?
2. Can you solve a similar problem where the angle expressions are different?
3. How would the equation change if the angles were not alternate interior angles but corresponding angles?
4. How does the value of \(x\) affect the overall geometry of the diagram?
5. What happens if the angles formed by the transversal are complementary instead of congruent?

### Tip:
Always double-check whether the angle expressions are congruent or supplementary before solving for \(x\).

Examine the diagram and determine the angle relationship, the value of x, and the measure of the angle in bold.

Learn how to solve for x using the alternate interior angles theorem. This problem involves setting two algebraic expressions equal to each other and solving the equation for the unknown variable x, followed by calculating the measure of the angle.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation