The problem involves parallel lines $m \parallel n$, and we are asked to find the value of $x$ given the angles in the diagram.

We can see:

• An angle of $116^\circ$ is given.
• $x^\circ$ is the angle we need to find.

Since $m \parallel n$ and the transversal intersects these parallel lines, the $x^\circ$ and $116^\circ$ angles are supplementary angles (interior angles on the same side of the transversal). Supplementary angles add up to $180^\circ$.

Thus: $x + 116^\circ = 180^\circ$

To find $x$: $x = 180^\circ - 116^\circ = 64^\circ$

So, the value of $x$ is $64^\circ$.

Would you like more details or have any questions?

5 Related Questions:

1. What are alternate interior angles and how do they relate to parallel lines?
2. How can we identify corresponding angles in a transversal setup?
3. What is the difference between supplementary and complementary angles?
4. How do we find unknown angles when multiple parallel lines are involved?
5. How does the angle sum property apply in different geometric setups?

Tip: In problems involving parallel lines and a transversal, look for relationships like corresponding, alternate, or interior angles to simplify your solution.