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The image you uploaded asks for the measure of \( \angle ABO \), denoted as \( x \).

In the diagram, \( \angle ABO \) and \( \angle OBC \) (which is given as \( 149^\circ \)) are adjacent angles that form a straight line along \( AC \), which is a straight line. Adjacent angles on a straight line are supplementary, meaning their measures sum to \( 180^\circ \).

Therefore, we can set up the equation:
\[
x + 149^\circ = 180^\circ
\]

To solve for \( x \):
\[
x = 180^\circ - 149^\circ = 31^\circ
\]

Thus, the measure of \( \angle ABO \) is \( 31^\circ \).

Would you like further clarification on this? Here are five related questions to explore this topic further:

1. What are supplementary angles and how are they used in geometry?
2. How do you find the missing angle in a triangle?
3. What is the difference between complementary and supplementary angles?
4. Can adjacent angles be anything other than supplementary on a straight line?
5. How do you solve for angles in more complex geometric figures, like polygons?

**Tip:** When working with adjacent angles, always check if they form a straight line or a right angle, as this helps determine their relationship quickly!

Learn how to find the measure of angle ABO using the supplementary angles concept. Understand the relationship between adjacent angles on a straight line and apply the formula to solve the problem. Suitable for students in Grades 6-8.

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