https://file.aiquickdraw.com/mathbot/file/1729127039649tttmxjkj.jpg

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.

Find the measure of the missing angles (d, e, and f) in the diagram provided. Angle 27°, angle 131°, and the missing angles are part of a system involving vertical and supplementary angles.

Learn how to calculate missing angles in a geometry problem using the concepts of vertical angles and supplementary angles. This problem involves finding the measures of angles d, e, and f, with given angles of 27° and 131°.

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