https://file.aiquickdraw.com/mathbot/file/1726651966320vwiazlen.jpg

From the diagram, we can observe that it involves angles formed by parallel lines and a transversal. Specifically, the two given angles are \( 3(a - 10)^\circ \) and \( 2a^\circ \), and the middle angle between them is a right angle (\(90^\circ\)).

We can set up the equation by recognizing that the sum of the angles along a straight line is \(180^\circ\).

The sum of the angles is:
\[
3(a - 10) + 90 + 2a = 180
\]

Now let's solve for \(a\).

### Step-by-step Solution:
1. Expand the first term:
   \[
   3(a - 10) = 3a - 30
   \]
   So the equation becomes:
   \[
   3a - 30 + 90 + 2a = 180
   \]

2. Combine like terms:
   \[
   (3a + 2a) + (-30 + 90) = 180
   \]
   \[
   5a + 60 = 180
   \]

3. Subtract 60 from both sides:
   \[
   5a = 120
   \]

4. Divide both sides by 5:
   \[
   a = 24
   \]

Thus, the value of \(a\) is \( \boxed{24} \).

Would you like any further clarification or details?

Here are some related questions to expand your understanding:
1. What properties of parallel lines and transversals did we use to set up this equation?
2. How do we know that the sum of angles on a straight line equals 180 degrees?
3. Can you apply this method to any diagram with parallel lines and transversals?
4. If the right angle wasn't present, how would that change the problem?
5. What would happen if one of the angles was given in terms of a different variable?

**Tip**: When working with angles formed by transversals, always look for relationships such as corresponding angles or alternate interior angles!

Write an equation and solve it for a which is shown in the following diagram.

Learn how to solve for a in a geometry problem that involves angles formed by parallel lines and a transversal. The sum of the angles is set to 180°, with step-by-step instructions provided. Suitable for students in Grades 8-10.

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