https://file.aiquickdraw.com/mathbot/file/1726096712402ezzrg2m5.jpg

The given diagram appears to show a parallelogram \( OLNM \), where two angles are labeled as:

- \( \angle LNM = (8x - 40)^\circ \)
- \( \angle LMN = (3x)^\circ \)

In a parallelogram, consecutive angles are supplementary, meaning their sum is 180°.

Thus, we can set up the equation:

\[
(8x - 40)^\circ + (3x)^\circ = 180^\circ
\]

Now, solving for \( x \):

\[
8x - 40 + 3x = 180
\]
\[
11x - 40 = 180
\]
\[
11x = 220
\]
\[
x = 20
\]

Thus, the value of \( x \) is \( 20 \).

Would you like more details on this solution, or do you have any questions?

Here are 5 related questions to expand on this topic:
1. What are the properties of a parallelogram?
2. How can we calculate the other angles in the parallelogram using the value of \( x \)?
3. What is the difference between consecutive and opposite angles in a parallelogram?
4. How would this change if the quadrilateral were a different type, such as a trapezoid?
5. Can you solve for the side lengths of the parallelogram if more information were provided?

**Tip:** Always remember that consecutive angles in a parallelogram are supplementary, and opposite angles are equal.

What is the value of x in the given parallelogram?

Solve for the value of x in a parallelogram with angles labeled as (3x)° and (8x - 40)°. Learn how consecutive angles in a parallelogram are supplementary, which helps solve for x. Suitable for students in Grades 8-10.

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