Let's analyze the angles in the image to find the missing angles $d$, $e$, and $f$.

Step-by-Step Solution:

1. Angle d:

   • The angle labeled $20^\circ$ and $d$ are vertically opposite angles. Since vertically opposite angles are always equal, we conclude: $d = 20^\circ$

2. Angle e:

   • The angle labeled $134^\circ$ and $e$ are supplementary angles (they form a straight line together). Supplementary angles sum to $180^\circ$, so: $e + 134^\circ = 180^\circ$ Solving for $e$: $e = 180^\circ - 134^\circ = 46^\circ$

3. Angle f:

   • The angles $f$ and $134^\circ$ are vertically opposite angles, which means they are also equal. Thus: $f = 134^\circ$

Final Answer:

• $d = 20^\circ$
• $e = 46^\circ$
• $f = 134^\circ$

Would you like a detailed breakdown of any step?

Here are 5 related questions:

1. What are alternate interior angles, and how do they differ from vertically opposite angles?
2. Can you find supplementary angles when multiple lines intersect at a point?
3. How do you find missing angles in a triangle when given two angles?
4. What is the difference between complementary and supplementary angles?
5. How are exterior angles of polygons related to their interior angles?

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