To find the value of $x$ in the given diagram, we can use the fact that the angles on a straight line sum up to 180°. In this case, angles $\angle DCE$, $\angle ACD$ (70°), and $\angle ECB$ (40°) together form a straight line at point $C$.

Thus, we can set up the equation:

$\angle ACD + \angle x + \angle ECB = 180^\circ$

Substitute the known values:

$70^\circ + x + 40^\circ = 180^\circ$

Simplifying:

$110^\circ + x = 180^\circ$

Now, solve for $x$:

$x = 180^\circ - 110^\circ$

$x = 70^\circ$

Thus, the value of $x$ is $70^\circ$.

Would you like further details or have any other questions?

Here are 5 related questions for further practice:

1. What is the sum of the interior angles of a triangle?
2. How do you calculate supplementary angles?
3. What are vertically opposite angles, and how are they related?
4. If the angle $\angle DCE$ were doubled, what would $x$ become?
5. Can you apply the exterior angle theorem to solve for angles in other cases?

Tip: Remember, angles on a straight line always add up to 180°, which is key in solving many geometry problems.