Please do #5. ### Geometry Exercises#### Using the Diagram of $\overline{QT}$1. **Given $m∠PQ = 130°$, find $m∠RQ$**.2. **Given $m∠PR = 100°$, find $m∠PQ$**.#### Find the Value of $x$. Show Your Work on #5.3. ![Diagram 3](https://i.imgur.com/VnSxwN3.png) - A circle with chords $\overline{PS}$ and $\overline{QR}$ intersecting inside the circle. - $ PS = 11 $4. ![Diagram 4](https://i.imgur.com/fZDFrFV.png) - A circle with chords $\overline{DE}$ and $\overline{FG}$ intersecting inside the circle. - $m∠C = 65°$5. ![Diagram 5](https://i.imgur.com/FC6Odmt.png) - A circle with chords $\overline{PQ}$ and $\overline{RS}$ intersecting inside the circle. - $ PQ = 9x - 3 $ - $ RS = 7x + 5 $#### Determine Whether $\overline{AB}$ is a Diameter of Each Circle. Explain Your Reasoning Using a Theorem.6. (a) ![Diagram 6a](https://i.imgur.com/Xg7RAfz.png) - A circle with lines $\overline{AB}$ and $\overline{MN}$. - $ AM = MB = 17 $ - $m∠MAB = 90°$ (b) ![Diagram 6b](https://i.imgur.com/AtozFN7.png) - A circle with lines $\overline{AB}$ and $\overline{MN}$. - $ AM = MB = 6 $ - $m∠MAB = 103°$---In these exercises, you will utilize your knowledge of circle theorems and properties to solve for angles and determine the diameters of specific circles. Ensure to show your work and provide justifications based on geometric principles and theorems.

If we join PS and SR, we can say that these two triangles are congruent. Therefore, PE = RE.

In Exercises 1 and 2, use the diagram of OT. 1. If mPQ = 130°, find mRQ. 2. If mPR = 100°, find mPQ. In Exercises 3-5, find the value of x. Show your work on #5. 3. 4. 65 5. R D. P. 7x + 5 9x 11 R 6. Determine whether AB is a diameter of each circle. Explain your reasoning using a theorem. a. b. M 17 103 B 17 N.

In Exercises 1 and 2, use the diagram of OT. 1. If mPQ = 130°, find mRQ. 2. If mPR = 100°, find mPQ. In Exercises 3-5, find the value of x. Show your work on #5. 3. 4. 65 5. R D. P. 7x + 5 9x 11 R 6. Determine whether AB is a diameter of each circle. Explain your reasoning using a theorem. a. b. M 17 103 B 17 N.

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter87: An Introduction To G- And M-codes For Cnc Programming

Section: Chapter Questions

Problem 23A: Write a G-code program for the counterclockwise arc with starting point (-40, -20), ending point...

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Question

Please do #5.

### Geometry Exercises

#### Using the Diagram of $\overline{QT}$

1. **Given $m∠PQ = 130°$, find $m∠RQ$**.

2. **Given $m∠PR = 100°$, find $m∠PQ$**.

#### Find the Value of $x$. Show Your Work on #5.

3. ![Diagram 3](https://i.imgur.com/VnSxwN3.png)
- A circle with chords $\overline{PS}$ and $\overline{QR}$ intersecting inside the circle.
- $ PS = 11 $

4. ![Diagram 4](https://i.imgur.com/fZDFrFV.png)
- A circle with chords $\overline{DE}$ and $\overline{FG}$ intersecting inside the circle.
- $m∠C = 65°$

5. ![Diagram 5](https://i.imgur.com/FC6Odmt.png)
- A circle with chords $\overline{PQ}$ and $\overline{RS}$ intersecting inside the circle.
- $ PQ = 9x - 3 $
- $ RS = 7x + 5 $

#### Determine Whether $\overline{AB}$ is a Diameter of Each Circle. Explain Your Reasoning Using a Theorem.

6. (a) ![Diagram 6a](https://i.imgur.com/Xg7RAfz.png)
- A circle with lines $\overline{AB}$ and $\overline{MN}$.
- $ AM = MB = 17 $
- $m∠MAB = 90°$

(b) ![Diagram 6b](https://i.imgur.com/AtozFN7.png)
- A circle with lines $\overline{AB}$ and $\overline{MN}$.
- $ AM = MB = 6 $
- $m∠MAB = 103°$

---

In these exercises, you will utilize your knowledge of circle theorems and properties to solve for angles and determine the diameters of specific circles. Ensure to show your work and provide justifications based on geometric principles and theorems.

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