Parallel Lines Cut by a Transversal Practice Problems Worksheet

Here are the step-by-step solutions for each problem on the worksheet.

1)
* Find x: The angle labeled $45^\circ$ and angle $x$ are vertical angles. Vertical angles are always equal.
* $x = 45$
* Find y: Angle $x$ and angle $y$ form a straight line (a linear pair), so they add up to $180^\circ$.
* $45 + y = 180$
* $y = 180 - 45$
* $y = 135$

2)
* Find x: Angle $x$ and the angle labeled $60^\circ$ are corresponding angles. Since the lines are parallel, corresponding angles are equal.
* $x = 60$
* Find y: Angle $x$ and angle $y$ are consecutive interior angles (they are on the same side of the transversal and between the parallel lines). They add up to $180^\circ$.
* $60 + y = 180$
* $y = 180 - 60$
* $y = 120$

3)
* Find x: Angle $x$ and the angle labeled $119^\circ$ form a straight line. They add up to $180^\circ$.
* $x + 119 = 180$
* $x = 180 - 119$
* $x = 61$
* Find y: Angle $y$ and the angle labeled $119^\circ$ are alternate interior angles. Alternate interior angles are equal.
* $y = 119$

4)
* Find x: Angle $x$ and the angle labeled $124^\circ$ are alternate exterior angles. These angles are equal.
* $x = 124$
* Find y: Angle $x$ and angle $y$ form a straight line. They add up to $180^\circ$.
* $124 + y = 180$
* $y = 180 - 124$
* $y = 56$

5)
* Find x: Angle $x$ and the angle labeled $43^\circ$ are alternate interior angles. These angles are equal.
* $x = 43$
* Find y: Angle $y$ and angle $x$ form a straight line. They add up to $180^\circ$.
* $y + 43 = 180$
* $y = 180 - 43$
* $y = 137$

6)
* Find x: Angle $x$ and the angle labeled $151^\circ$ are corresponding angles. These angles are equal.
* $x = 151$
* Find y: Angle $x$ and angle $y$ form a straight line. They add up to $180^\circ$.
* $151 + y = 180$
* $y = 180 - 151$
* $y = 29$

Final Answer:
1) x = 45, y = 135
2) x = 60, y = 120
3) x = 61, y = 119
4) x = 124, y = 56
5) x = 43, y = 137
6) x = 151, y = 29