To find the values of the five unknown angles $a$, $b$, $c$, $d$, and $e$, let's analyze the diagram using the given angles and properties of parallel lines and transversals.

Given:

• $\angle d = 62^\circ$
• $\angle c = 43^\circ$

Steps:

1. Identify Angle Relationships with Parallel Lines: Since the lines in blue appear to be parallel and are cut by transversals, we can use properties such as corresponding angles, alternate interior angles, and supplementary angles.

2. Find $\angle e$:

   • Since $\angle d$ and $\angle e$ are on a straight line, they are supplementary.
   • So, $\angle e = 180^\circ - \angle d = 180^\circ - 62^\circ = 118^\circ$.

3. Find $\angle b$:

   • $\angle b$ is vertically opposite $\angle d$, which means $\angle b = 62^\circ$.

4. Find $\angle a$:

   • $\angle a$ corresponds to $\angle c$ since they are on opposite parallel lines.
   • Therefore, $\angle a = \angle c = 43^\circ$.

5. Find $\angle c$ (already known as 43°):

   • $\angle c$ was given directly, so $\angle c = 43^\circ$ as stated.

Summary of the Angles:

• $\angle a = 43^\circ$
• $\angle b = 62^\circ$
• $\angle c = 43^\circ$
• $\angle d = 62^\circ$
• $\angle e = 118^\circ$

Would you like a deeper explanation for any of these steps or have any other questions?

Here are 5 related questions that may help deepen understanding:

1. How do corresponding angles in parallel lines relate to each other?
2. What is the difference between vertically opposite angles and corresponding angles?
3. How would the values change if one of the angles were altered?
4. What other geometric properties apply when two parallel lines are intersected by a transversal?
5. Can these principles be applied to non-parallel lines?

Tip: Always look for corresponding and alternate angles when dealing with parallel lines cut by a transversal, as they often provide shortcuts to finding unknown angles.