https://file.aiquickdraw.com/mathbot/file/1726125965687jcmqke52.jpg

The image presents a pair of parallel lines cut by a transversal, and we are tasked with determining the value of \( a \).

### Step-by-step solution:

1. **Identify the relationships**:
   - The angles \( 43^\circ \) and \( 136^\circ \) are consecutive interior angles along the transversal, but they also provide valuable information on the third angle \( a \).
   - \( 136^\circ \) and \( a^\circ \) form a linear pair (on a straight line), meaning they are supplementary.

2. **Use supplementary angle rule**:
   - Two angles that form a straight line sum up to \( 180^\circ \). Therefore, we use the equation:
     \[
     136^\circ + a = 180^\circ
     \]

3. **Solve for \( a \)**:
   \[
   a = 180^\circ - 136^\circ = 44^\circ
   \]

Thus, the value of \( a \) is \( \boxed{44^\circ} \).

Would you like further explanation or have any other questions?

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Here are 5 related questions for practice:

1. How do you find the value of an angle when given two parallel lines and a transversal?
2. What is the difference between alternate interior and corresponding angles?
3. If \( a \) was on the opposite side of the transversal, how would its value change?
4. How can we determine the relationship between angles when more than one transversal is involved?
5. What are vertical angles, and how do they relate to parallel lines?

**Tip**: Always remember that corresponding angles formed by a transversal intersecting parallel lines are congruent!

What is the value of a in the given parallel lines and transversal diagram with angles 43° and 136°?

Learn how to find the value of angle a in a parallel lines and transversal diagram where the given angles are 43° and 136°. This problem covers the use of supplementary angles to determine missing angle values, suitable for students in Grades 7-9.

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