We are given the angles:

• $\angle ABC = 160^\circ$
• $\angle DBC = 50^\circ$
• $\angle ABD = x^\circ$

Since $\angle ABC$ is the sum of $\angle ABD$ and $\angle DBC$, we can write:

$x + 50^\circ = 160^\circ$

Solving for $x$:

$x = 160^\circ - 50^\circ$

$x = 110^\circ$

So, the value of $x$ is 110°.

Would you like a more detailed explanation or any clarifications?

Here are five related questions to explore further:

1. How do you identify supplementary and complementary angles?
2. What is the angle addition postulate, and how is it used in geometry?
3. How can you determine unknown angles in a triangle using given angles?
4. How do linear pairs and vertical angles relate to each other?
5. How can exterior angles of polygons be used to solve angle problems?

Tip: Always check if the given angles form a straight line or are part of a triangle to apply the correct angle properties.