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To solve the problem of finding the measure of angle \( A \), let's analyze the diagram.

1. The two angles adjacent to angle \( A \) are labeled as \( 5x \) and \( 4x \), and there is a right angle (90°) formed by these two angles, indicating that:
   \[
   5x + 4x = 90^\circ
   \]
   This equation comes from the fact that the sum of the angles around a straight line (from the right angle) is 90°.

2. Simplifying:
   \[
   9x = 90^\circ
   \]
   Solving for \( x \):
   \[
   x = \frac{90^\circ}{9} = 10^\circ
   \]

3. Now, we know that \( x = 10^\circ \). Angle \( A \) is labeled as \( 4x \), so:
   \[
   A = 4x = 4 \times 10^\circ = 40^\circ
   \]

Thus, the measure of angle \( A \) is **40°**.

Would you like any further details or clarification?

### Related Questions:
1. What is the sum of the angles formed at a straight line intersection?
2. How can you verify that the adjacent angles sum up to 90° in this diagram?
3. What happens to the calculation if the angle labeled 90° was not a right angle?
4. Can we use this method to calculate angles in a triangle?
5. What are supplementary angles, and how are they related to this problem?

### Tip:
Always check for right angles in geometry problems, as they give important information about the sum of adjacent angles.

Determine the measure of angle A using the concepts of linear pairs and supplementary angles. Learn how to solve for unknowns by setting up and solving equations involving geometric principles. Suitable for Grades 6-8.

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