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This image shows a diagram with two parallel lines crossed by a transversal. The goal is to find the value of \( x \). From the diagram, the angle expressions are:

- One angle is given as \( 141^\circ \).
- The other angle is expressed as \( (2x + 1)^\circ \).

These two angles are **co-interior** angles, meaning they are on the same side of the transversal and between the two parallel lines. Co-interior angles are **supplementary**, which means their sum is \( 180^\circ \).

We can set up the equation as follows:
\[
(2x + 1) + 141 = 180
\]

Now, let's solve for \( x \). 

\[
2x + 1 + 141 = 180
\]
\[
2x + 142 = 180
\]
\[
2x = 180 - 142
\]
\[
2x = 38
\]
\[
x = \frac{38}{2}
\]
\[
x = 19
\]

So, the value of \( x \) is \( 19 \).

Would you like more details or have any further questions?

Here are 5 related questions to explore:
1. What are the other types of angle relationships formed by a transversal crossing parallel lines?
2. How do alternate interior angles behave with parallel lines?
3. Can you solve for \( x \) if the angles were alternate exterior instead of co-interior?
4. What happens if the transversal crosses two non-parallel lines? How would the angles change?
5. How can we prove that co-interior angles are supplementary?

**Tip:** When working with angles and transversals, remember to carefully observe whether the lines are parallel, as it changes the relationships between the angles.

Find the value of x based on the angles (2x + 1)° and 141° formed by a transversal crossing two parallel lines.

Find the value of x in this geometry problem where two parallel lines are crossed by a transversal, forming co-interior angles of (2x + 1)° and 141°. Learn the step-by-step solution and understand the properties of co-interior angles, suitable for Grades 8-10.

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