The image contains a geometry problem involving intersecting lines $a$, $b$, $c$, and $d$, and asks to determine the values of the angles $x$, $y$, and $z$. Let's analyze the provided information step by step:

Given Information:

1. Angle of $124^\circ$ is marked at the top where line $a$ intersects another line.
2. Angle $42^\circ$ is adjacent to the $124^\circ$ angle (these are supplementary).
3. Angle $53^\circ$ is near the center where the lines meet.
4. Angle $95^\circ$ is given on the right side.
5. Angle $39^\circ$ is given near the bottom.
6. A vertical line labeled $x^\circ$ needs to be determined.
7. Another angle labeled $y^\circ$ is shown, needing calculation.
8. Another angle labeled $z^\circ$ is shown.

Step-by-Step Solution:

1. Find $x$:

At the intersection of lines, the angle marked as $x^\circ$ is vertically opposite to the angle $124^\circ$. Vertically opposite angles are always equal. Hence: $x = 124^\circ$

2. Find $y$:

The angle $y^\circ$ and $95^\circ$ are corresponding angles formed by the transversal. Hence, they are equal: $y = 95^\circ$

3. Find $z$:

To find $z$, we can use the fact that it forms a straight line with the adjacent angle $39^\circ$. These angles are supplementary, meaning their sum is $180^\circ$: $z + 39^\circ = 180^\circ$ $z = 180^\circ - 39^\circ = 141^\circ$

Final Answers:

$x = 124^\circ, \quad y = 95^\circ, \quad z = 141^\circ$

Let me know if you'd like more details or have any further questions.

Here are 5 related questions to further your understanding:

1. What are vertically opposite angles, and why are they always equal?
2. How do corresponding angles help in solving geometry problems involving transversals?
3. What is the relationship between supplementary angles?
4. Can you identify any alternate interior angles in the given diagram?
5. How would the problem change if the lines were not parallel?

Tip: When working with parallel lines, always look for corresponding, alternate interior, or vertically opposite angles, as they simplify finding unknown angles!