To find the value of $x$ in this triangle, let's use the fact that the sum of the angles in a triangle is always $180^\circ$.

The triangle has three angles:

1. $78^\circ$
2. $42^\circ$
3. $x^\circ$

Since the sum of all angles in a triangle is $180^\circ$, we can write the equation: $78 + 42 + x = 180$

Adding $78$ and $42$: $120 + x = 180$

Now, subtract $120$ from both sides: $x = 60$

So, the value of $x$ is $60^\circ$.

Would you like a deeper explanation or have any questions?

Here are some related questions you might find interesting:

1. What is the rule for finding the missing angle in any triangle?
2. How can we determine if a triangle is acute, obtuse, or right?
3. What are the types of triangles based on their angles and sides?
4. Can the sum of two angles in a triangle ever exceed $180^\circ$?
5. How would the approach change if this was an exterior angle of a triangle?

Tip: Remember that the sum of interior angles in any triangle is always $180^\circ$.