https://file.aiquickdraw.com/mathbot/file/17290180400021o7i88gp.jpg

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.

What is the measure of angle ABC if angle DBC is 57° and both angles form a linear pair?

This page explains how to solve for angle ABC when it forms a linear pair with angle DBC (57°). The solution involves using the linear pair and supplementary angle theorems, which state that the sum of the two angles is always 180°. This problem is appropriate for students in Grades 7-9.

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