This problem involves angles around a point. The sum of all angles around a point is always 360°. We are given two of the angles: 46° and 103°, and we need to find the angles labeled $d$, $e$, and $f$.

Steps to Solve:

1. Find $f$:

   • $f$ is vertically opposite to the angle 103°.
   • Vertically opposite angles are equal, so: $f = 103^\circ$

2. Find $d$:

   • $d$ is vertically opposite to the angle 46°.
   • Vertically opposite angles are also equal, so: $d = 46^\circ$

3. Find $e$:

   • The sum of angles around the point is 360°.
   • We already know the values of three angles: 46°, 103°, and 103° (from $f$).
   • The remaining angle $e$ can be found by subtracting the sum of the known angles from 360°: $e = 360^\circ - (46^\circ + 103^\circ + 103^\circ) = 360^\circ - 252^\circ = 108^\circ$

Final Answers:

• $d = 46^\circ$
• $e = 108^\circ$
• $f = 103^\circ$

Let me know if you need more details or further clarifications!

Here are 5 related questions:

1. What is the sum of all angles at a point?
2. How do vertically opposite angles relate to each other?
3. Can the sum of angles on a straight line be used to solve this?
4. What is the complementary relationship between adjacent angles?
5. How can we check if our calculated angles are correct?

Tip: Vertically opposite angles are always equal, which simplifies many geometric problems!