https://file.aiquickdraw.com/mathbot/file/17263589282567zheq95h.jpg

In this diagram, we are given a few angles and asked to find the missing ones: \(d\), \(e\), and \(f\). Let's analyze the relationships:

1. **Angle \(d\)**: The angle marked \(d\) is a right angle, shown by the symbol indicating 90°. Therefore, \(d = 90^\circ\).

2. **Angle \(e\)**: Angle \(e\) forms a linear pair with the angle marked \(72^\circ\). Linear pairs are supplementary, meaning their sum is \(180^\circ\). Hence, we can calculate \(e\) as:
   \[
   e = 180^\circ - 72^\circ = 108^\circ
   \]

3. **Angle \(f\)**: Angle \(f\) is vertically opposite to the given \(72^\circ\) angle. Vertically opposite angles are equal, so:
   \[
   f = 72^\circ
   \]

### Final Answers:
- \(d = 90^\circ\)
- \(e = 108^\circ\)
- \(f = 72^\circ\)

Would you like more details or have any further questions?

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Here are 5 related questions to think about:
1. What are vertically opposite angles, and why are they equal?
2. How do you calculate the measure of an angle in a linear pair?
3. What are complementary and supplementary angles?
4. Can a triangle have a 90° angle and still have two equal angles? Why or why not?
5. How can the concept of angle bisectors help in solving angle problems?

**Tip:** Remember, linear pairs always sum to 180°, and vertically opposite angles are always equal!

Find the measure of the missing angles: d, e, and f, with a given angle of 72 degrees.

Learn how to calculate missing angles in a diagram with a linear pair and vertically opposite angles. With a given 72° angle, discover how to find angles d, e, and f. This problem covers the Linear Pair Theorem and Vertically Opposite Angle Theorem. Suitable for Grades 6-8.

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