https://file.aiquickdraw.com/mathbot/file/1725443730290zpqv2ciq.jpg

The image shows a diagram of angles on a straight line. Let's analyze and solve for \(a\).

### Information from the Diagram:
- The angle labeled \(160^\circ\) is a straight angle, part of a pair of angles that sum up to \(180^\circ\).
- The angle adjacent to it is a right angle, \(90^\circ\).
- The angle on the left side of the line is labeled as \((5a)^\circ\).

### Step-by-Step Solution:
1. The total sum of angles on a straight line is \(180^\circ\).
2. The two angles adjacent to each other sum up to form a straight line:
   \[
   (5a)^\circ + 160^\circ = 180^\circ
   \]
3. Solve for \(a\):
   \[
   5a + 160 = 180
   \]
   \[
   5a = 180 - 160
   \]
   \[
   5a = 20
   \]
   \[
   a = \frac{20}{5}
   \]
   \[
   a = 4
   \]

### Conclusion:
The value of \(a\) is \(4^\circ\).

Would you like more details on this, or do you have any questions? Here are some related questions to further your understanding:

1. What is the sum of angles around a point?
2. How do you calculate the angle opposite to a given angle on a straight line?
3. If \(a\) were doubled, what would the new angle be?
4. What would happen to \(a\) if the angle \(160^\circ\) changed to \(150^\circ\)?
5. How do alternate and corresponding angles relate to angles on a straight line?

**Tip:** Always remember that angles on a straight line add up to \(180^\circ\), a fundamental property in geometry.

The image shows a diagram of angles on a straight line. Solve for the value of 'a'.

Learn how to solve for the variable 'a' in a geometry problem involving angles on a straight line. This problem involves using the sum of angles on a straight line theorem, suitable for students in Grades 6-8.

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