The image shows two angles forming a linear pair. A linear pair consists of two adjacent angles whose non-common sides form a straight line, meaning the sum of the two angles is always $180^\circ$.

In the diagram:

• $\angle ABC$ is the unknown angle.
• $\angle DBC = 57^\circ$.

Since $\angle ABC$ and $\angle DBC$ form a linear pair, we use the equation: $\angle ABC + \angle DBC = 180^\circ$

Substituting the known value: $\angle ABC + 57^\circ = 180^\circ$

Solving for $\angle ABC$: $\angle ABC = 180^\circ - 57^\circ = 123^\circ$

Thus, $\angle ABC = 123^\circ$.

Would you like further details or have any questions?

Here are 5 related questions:

1. What are supplementary angles, and how do they relate to linear pairs?
2. How can we identify angles that form a linear pair in a complex figure?
3. Can two angles be adjacent but not form a linear pair?
4. What happens when three or more angles share a common vertex on a straight line?
5. How do we use algebra to solve for unknown angles in geometric figures?

Tip: Always check whether angles form special relationships (like linear pairs or complementary angles) to simplify calculations.