To solve for $x$ in the given triangle, we can use the fact that the sum of the angles in any triangle is $180^\circ$. The angles provided are $70^\circ$, $60^\circ$, and $8x + 2$.

The equation for the sum of the angles in the triangle is:

$70^\circ + 60^\circ + (8x + 2) = 180^\circ$

Let's simplify and solve this equation:

$130^\circ + (8x + 2) = 180^\circ$

$8x + 2 = 180^\circ - 130^\circ$

$8x + 2 = 50^\circ$

Now, subtract 2 from both sides:

$8x = 48^\circ$

Finally, divide by 8:

$x = 6$

Thus, the value of $x$ is 6.

Would you like more details or have any further questions? Here are 5 related questions to consider:

1. What is the sum of the interior angles of a triangle?
2. How can you solve for an unknown angle in a triangle when given the other two?
3. If one of the angles in the triangle was $90^\circ$, what type of triangle would it be?
4. How do you determine if a triangle is isosceles based on its angles?
5. What are the properties of an equilateral triangle?

Tip: Always remember, the sum of the angles in any triangle is always $180^\circ$, which is essential for solving many geometry problems!