Let's analyze the given diagram and determine the missing angles $d$, $e$, and $f$.

1. Angle $d$:

   • The angle adjacent to $87^\circ$ on a straight line must sum to $180^\circ$ (since they are supplementary). $d = 180^\circ - 87^\circ = 93^\circ$

2. Angle $e$:

   • The angle adjacent to $70^\circ$ along the same straight line also must sum to $180^\circ$. Thus, $e = 180^\circ - 70^\circ = 110^\circ$

3. Angle $f$:

   • Angles $e$ and $f$ are vertically opposite, so they must be equal. Therefore, $f = 110^\circ$

Final Answers:

• $d = 93^\circ$
• $e = 110^\circ$
• $f = 110^\circ$

Would you like more details or clarification on any part of this solution?

Here are 5 follow-up questions related to this concept:

1. What are vertically opposite angles and how do we identify them?
2. How can you determine if two angles are supplementary?
3. What is the sum of all angles formed by intersecting lines?
4. How do you know when two angles are congruent?
5. Can angles on a straight line ever sum to more than 180 degrees?

Tip: Always check if lines are straight to confirm supplementary angles in problems involving angles.