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.