We are tasked with finding the measures of the missing angles $d$, $e$, and $f$. Let’s break it down:

Step 1: Vertical angles

Vertical angles are equal. In the diagram, angle $131^\circ$ and angle $d$ are vertical angles, so: $d = 131^\circ$

Step 2: Linear pair (Supplementary angles)

A linear pair of angles is supplementary, meaning the angles add up to $180^\circ$. Angle $e$ and $131^\circ$ are adjacent and form a linear pair, so: $e + 131^\circ = 180^\circ$ $e = 180^\circ - 131^\circ = 49^\circ$

Step 3: Another linear pair

Similarly, angle $f$ and $27^\circ$ form a linear pair. Thus: $f + 27^\circ = 180^\circ$ $f = 180^\circ - 27^\circ = 153^\circ$

Summary:

• $d = 131^\circ$
• $e = 49^\circ$
• $f = 153^\circ$

Would you like any further details or clarification?

Here are 5 related questions you might want to explore:

1. What is the sum of all angles around a point?
2. How do you find the measure of angles using complementary angles?
3. Can adjacent angles ever be equal?
4. How are vertical angles and linear pairs different in properties?
5. What are alternate interior angles, and how are they related to this problem?

Tip: Always remember that vertical angles are congruent, and adjacent angles that form a straight line are supplementary.