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The problem you’ve provided is about finding missing angle measures based on the diagram and information given. The information at the top tells us that several angles, including \( \angle FHE \), \( \angle BHG \), and \( \angle AHF \), are right angles (90°), and this will help solve the problems.

Let's go through the questions one by one:

**17. If \( m\angle 3 = 30^\circ \), then \( m\angle 6 = ? \)**

From the diagram, \( \angle 3 \) and \( \angle 6 \) appear to be vertically opposite angles. Vertically opposite angles are always equal, so:

\[
m\angle 6 = 30^\circ
\]

**18. If \( m\angle BHF = 115^\circ \), then \( m\angle 3 = ? \)**

The angle \( \angle BHF \) and \( \angle 3 \) are supplementary angles because they form a linear pair along the straight line. Supplementary angles add up to 180°:

\[
m\angle 3 = 180^\circ - 115^\circ = 65^\circ
\]

**19. If \( m\angle 6 = 27^\circ \), then \( m\angle 1 = ? \)**

From the diagram, \( \angle 6 \) and \( \angle 1 \) are adjacent and form a straight line (they are supplementary). Thus:

\[
m\angle 1 = 180^\circ - 27^\circ = 153^\circ
\]

**20. If \( m\angle DHF = 133^\circ \), then \( m\angle CHG = ? \)**

The angles \( \angle DHF \) and \( \angle CHG \) are also supplementary since they form a linear pair. So:

\[
m\angle CHG = 180^\circ - 133^\circ = 47^\circ
\]

**21. If \( m\angle 3 = 32^\circ \), then \( m\angle 2 = ? \)**

From the diagram, \( \angle 3 \) and \( \angle 2 \) are vertically opposite, and vertically opposite angles are equal. Therefore:

\[
m\angle 2 = 32^\circ
\]

---

Would you like a more detailed explanation for any of these, or do you have other questions?

Here are some related questions to expand your understanding:

1. What is the relationship between vertically opposite angles?
2. How do you determine if two angles are supplementary?
3. Can adjacent angles be both supplementary and complementary?
4. How are angles around a point related to each other?
5. Why is it important to recognize linear pairs in geometry problems?

**Tip**: Always check if angles are vertically opposite or part of a linear pair in diagrams involving intersecting lines, as these relationships simplify calculations.

If m∠3 = 30°, then m∠6 = ?. If m∠BHF = 115°, then m∠3 = ?. If m∠6 = 27°, then m∠1 = ?. If m∠DHF = 133°, then m∠CHG = ?. If m∠3 = 32°, then m∠2 = ?.

Learn how to find missing angle measures based on vertically opposite and supplementary angle relationships. This problem set involves geometry concepts like vertically opposite angles, linear pairs, and how to calculate unknown angles. Suitable for Grades 7-9.

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