From the image, we are given three angles with their expressions:

• $m \angle AOB = (5x - 9)^\circ$
• $m \angle BOC = (7x + 16)^\circ$
• $m \angle COD = (2x + 12)^\circ$

These angles are adjacent, meaning that their sum should equal 180° (since they form a straight line, as indicated in the diagram).

The equation to solve will be:

$(5x - 9) + (7x + 16) + (2x + 12) = 180$

Let's simplify and solve for $x$:

1. Combine like terms: $(5x + 7x + 2x) + (-9 + 16 + 12) = 180$ $14x + 19 = 180$

2. Subtract 19 from both sides: $14x = 161$

3. Divide by 14: $x = \frac{161}{14} \approx 11.5$

Thus, $x \approx 11.5$.

Now you can substitute this value back into each expression to find the angle measures if needed.

Would you like the angle measures or further details on any step?

Relative questions:

1. What is the sum of angles in a straight line?
2. How do you check the accuracy of angle calculations?
3. Can adjacent angles be supplementary in all cases?
4. How do you simplify and solve linear equations?
5. How does the concept of adjacent angles apply to geometry?

Tip: When working with equations involving angles, always verify if the angles are complementary or supplementary to determine their sum properly.