To solve for the missing angles $d$, $e$, and $f$, we need to analyze the geometric relationships in the diagram.

Step-by-Step Solution:

1. Angle $d$:

   • Notice that angle $d$ is adjacent to a right angle. Therefore, angle $d = 90^\circ$.

2. Angle $e$:

   • Angles $e$ and the $151^\circ$ angle form a linear pair (they are on a straight line).
   • Therefore, $e + 151^\circ = 180^\circ$.
   • Solving for $e$:
     $e = 180^\circ - 151^\circ = 29^\circ.$

3. Angle $f$:

   • Angles $e$ and $f$ are vertically opposite angles, so they are equal.
   • Therefore, $f = e = 29^\circ$.

Final Answer:

• $d = 90^\circ$
• $e = 29^\circ$
• $f = 29^\circ$

Would you like more details or have any other questions?

Related Questions:

1. How do you find the measure of a supplementary angle?
2. What are vertically opposite angles and why are they equal?
3. Can you explain why the sum of angles on a straight line is always $180^\circ$?
4. How do you determine the type of angles formed by intersecting lines?
5. What is the definition of a linear pair of angles?

Tip: Remember, angles that are on a straight line always add up to $180^\circ$.