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The diagram shows two parallel lines cut by a transversal, and we are tasked with finding the values of the angles \(a\), \(b\), \(c\), \(d\), \(e\), \(f\), and \(g\) based on the given angle of \(54^\circ\).

Here’s how to proceed using properties of parallel lines and transversals:

### Step 1: Identify angle relationships
- **Vertical angles** are equal (formed by intersecting lines).
- **Corresponding angles** are equal (angles on the same side of the transversal and in corresponding positions).
- **Alternate interior angles** are equal (angles on opposite sides of the transversal but inside the parallel lines).
- **Supplementary angles** sum to \(180^\circ\) (angles on a straight line).

### Step 2: Calculate each angle

- \(a\) is vertically opposite to \(54^\circ\), so:
  \[
  a = 54^\circ
  \]

- \(b\) and \(c\) form a straight line with \(54^\circ\), so they are supplementary:
  \[
  b = 180^\circ - 54^\circ = 126^\circ
  \]
  By vertical angle property, \(c = 126^\circ\).

- \(d\) is corresponding to \(54^\circ\) (since the two parallel lines are cut by a transversal), so:
  \[
  d = 54^\circ
  \]

- \(e\) is vertically opposite to \(d\), so:
  \[
  e = 54^\circ
  \]

- \(f\) is corresponding to \(b\), so:
  \[
  f = 126^\circ
  \]

- \(g\) is vertically opposite to \(f\), so:
  \[
  g = 126^\circ
  \]

### Final values:
\[
a = 54, \, b = 126, \, c = 126, \, d = 54, \, e = 54, \, f = 126, \, g = 126
\]

Would you like more details or clarifications?

### Relative Questions:
1. How do you identify corresponding angles in parallel line diagrams?
2. What are vertical angles, and why are they always equal?
3. Can alternate interior angles be used to find unknown angles in this type of diagram?
4. How do supplementary angles help solve transversal problems?
5. Why do parallel lines ensure that certain angle relationships hold?

### Tip:
Always remember that corresponding angles and alternate interior angles are key when working with parallel lines and transversals.

Find the values of a, b, c, d, e, f, and g based on the given diagram showing two parallel lines cut by a transversal, with one angle of 54° provided.

Learn how to solve a problem involving two parallel lines cut by a transversal where one angle is given as 54°. Discover how to calculate the remaining angles using vertical angles, corresponding angles, and supplementary angles theorems. Ideal for students in Grades 8-10.

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