Problem Analysis:
The image shows two parallel lines, \( a \) and \( b \), with a transversal line \( t \) intersecting them. The angle formed between the transversal \( t \) and line \( a \) is given as \( 60^\circ \). Another angle, labeled as \( 8x - 4 \), is formed between the transversal \( t \) and line \( b \). Since \( a \) and \( b \) are parallel, the angles formed by the transversal with these lines have specific relationships.
We need to solve for \( x \) using the geometric properties of parallel lines and transversals.
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Step-by-Step Solution:
1.
Identify the Relationship Between the Angles:
- When a transversal intersects two parallel lines, corresponding angles are equal.
- The angle \( 60^\circ \) on line \( a \) corresponds to the angle \( 8x - 4 \) on line \( b \) because they are corresponding angles.
2.
Set Up the Equation:
- Since corresponding angles are equal, we can write:
\[
8x - 4 = 60
\]
3.
Solve for \( x \):
- Add 4 to both sides of the equation:
\[
8x - 4 + 4 = 60 + 4
\]
\[
8x = 64
\]
- Divide both sides by 8:
\[
x = \frac{64}{8}
\]
\[
x = 8
\]
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Final Answer:
\[
\boxed{8}
\]
Parent Tip: Review the logic above to help your child master the concept of parallel line cut by a transversal worksheet.
