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In this problem, we are given a diagram with two adjacent angles formed by a straight line at point B. The angles are labeled as follows:

- \(\angle ABC = x + 20\)
- \(\angle CBD = x - 18\)

Since these angles form a linear pair, they are supplementary. This means the sum of their measures must be equal to \(180^\circ\).

To solve for \(x\):

\[
(x + 20) + (x - 18) = 180
\]

Simplify the equation:

\[
x + 20 + x - 18 = 180
\]

\[
2x + 2 = 180
\]

Subtract 2 from both sides:

\[
2x = 178
\]

Divide by 2:

\[
x = 89
\]

Now, substitute \(x = 89\) back into the expressions for the angles:

\[
\angle ABC = 89 + 20 = 109^\circ
\]
\[
\angle CBD = 89 - 18 = 71^\circ
\]

Thus, the measures of the angles are:
- \(\angle ABC = 109^\circ\)
- \(\angle CBD = 71^\circ\)

Both angles add up to \(109^\circ + 71^\circ = 180^\circ\), confirming the solution is correct.

Would you like more details or have any questions?

Here are some related questions:
1. What is the definition of supplementary angles?
2. How do adjacent angles relate to linear pairs?
3. Can two acute angles form a supplementary pair?
4. What are complementary angles and how are they different from supplementary angles?
5. How would the problem change if the angles were complementary instead of supplementary?

**Tip:** Always check if angles form a straight line; if they do, their sum should be \(180^\circ\).

Find the measure of angle ABC if the angles formed by point B on a straight line are x+20 and x-18, and the angles are adjacent and form a linear pair.

This problem involves finding the measures of angles in a linear pair, where the angles are represented by x+20 and x-18. Using algebraic expressions and the concept of supplementary angles, this problem is suited for students in Grades 7-9.

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