The image shows a question where you are tasked to find the missing angles $d$, $e$, and $f$ based on the given angle values of $27^\circ$ and $131^\circ$.

Let's solve for the missing angles step by step:

1. Angle $d$: Since $d$ and $131^\circ$ form a linear pair (they are on a straight line), they must add up to $180^\circ$. $d + 131^\circ = 180^\circ$ Solving for $d$: $d = 180^\circ - 131^\circ = 49^\circ$

2. Angle $e$: The angle $e$ is vertically opposite to the angle $131^\circ$, and vertically opposite angles are equal. Thus, $e = 131^\circ$

3. Angle $f$: Angle $f$ is vertically opposite to the $27^\circ$ angle. Again, vertically opposite angles are equal. So, $f = 27^\circ$

Final answers:

• $d = 49^\circ$
• $e = 131^\circ$
• $f = 27^\circ$

Would you like further details on any part of the explanation?

Here are five related questions you might explore:

1. What are vertically opposite angles, and why are they always equal?
2. How do we use the concept of linear pairs to solve for unknown angles?
3. What are supplementary angles, and how do they differ from complementary angles?
4. How would the calculation change if the lines were not straight but formed a triangle?
5. Can angles in parallel lines and transversal situations also be solved using these principles?

Tip: Always remember, angles on a straight line add up to $180^\circ$, and vertically opposite angles are always equal.