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. 4. 65 5. R 3. 7x + 5 9x 11 R. 6. Determine whether AB is a diameter of each circle. Explain your reasoning using a theorem. M b. M. a. 17 103 A 17 N. 3. P.
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. 4. 65 5. R 3. 7x + 5 9x 11 R. 6. Determine whether AB is a diameter of each circle. Explain your reasoning using a theorem. M b. M. a. 17 103 A 17 N. 3. P.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Please do #2.
- Circle with a central point T and lines intersecting the circle at points P, Q, R, and S, whereas PT = 7 and TR = 7, perpendicular lines form at T to PQ and RS, respectively, segment ST = 11.
4. 
- Circle centered at point C with lines intersecting the circle at points D, E, G, and F. A line DG intersects DE at point C, with angle DEC = 65°.
- C is the center of this circle.
5. 
- Circle with a central point T and lines intersecting the circle at points P, Q, R, and S. Angles PQR and QRS are expressed algebraically with 9x − 3 for PQR and 7x + 5 for QRS.
#### Determine whether \(\overline{AB}\) is a diameter of each circle. Explain your reasoning using a theorem.
6a. 
- Circle centered at M with segments AM, BN, and AB labeled.
- AM and MB both measure 17, and the line AB spans the circle through the center and forms a right angle at M.
- Angle ANM is 90°.
6b. 
- Circle centered at M with segments AN, BN, and AB labeled.
- Lines AN and BM intersect at an interior point forming a quadrilateral ANMB, with AN = 6, BM = 6, and angle ANM = 103°.
### Solution Walkthrough:
1. **Exercises 1 and 2 solutions**:
Use the properties of circles and the relationships between the angles to calculate the others.
2. **Exercises 3–5 solutions**:
Find the value of x by using circle theorems and angle relationships within the circle.
3. **](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c728cf8-64c2-4469-9e88-bc7c5dc6b71c%2F7620aded-1340-4795-8b91-dd2f586da630%2Fvdut2n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Circle Geometry Exercises
#### In Exercises 1 and 2, use the diagram of ∠QT:
1. If m∠PQ = 130°, find m∠RQ.
2. If m∠PR = 100°, find m∠PQ.
#### In Exercises 3–5, find the value of x. Show your work on #5.
3. 
- Circle with a central point T and lines intersecting the circle at points P, Q, R, and S, whereas PT = 7 and TR = 7, perpendicular lines form at T to PQ and RS, respectively, segment ST = 11.
4. 
- Circle centered at point C with lines intersecting the circle at points D, E, G, and F. A line DG intersects DE at point C, with angle DEC = 65°.
- C is the center of this circle.
5. 
- Circle with a central point T and lines intersecting the circle at points P, Q, R, and S. Angles PQR and QRS are expressed algebraically with 9x − 3 for PQR and 7x + 5 for QRS.
#### Determine whether \(\overline{AB}\) is a diameter of each circle. Explain your reasoning using a theorem.
6a. 
- Circle centered at M with segments AM, BN, and AB labeled.
- AM and MB both measure 17, and the line AB spans the circle through the center and forms a right angle at M.
- Angle ANM is 90°.
6b. 
- Circle centered at M with segments AN, BN, and AB labeled.
- Lines AN and BM intersect at an interior point forming a quadrilateral ANMB, with AN = 6, BM = 6, and angle ANM = 103°.
### Solution Walkthrough:
1. **Exercises 1 and 2 solutions**:
Use the properties of circles and the relationships between the angles to calculate the others.
2. **Exercises 3–5 solutions**:
Find the value of x by using circle theorems and angle relationships within the circle.
3. **
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