Please do #1. ### Educational Exercise on Circle Geometry#### In Exercises 1 and 2, use the diagram of ∠OT.1. **Given**: $ m\angle PQ = 130^\circ $ - **Find**: $ m\angle RQ $ 2. **Given**: $ m\angle PR = 100^\circ $ - **Find**: $ m\angle PQ $#### In Exercises 3–5, find the value of $ x $. Show your work on #5.3. **Diagram Description**: - A circle with center $ T $. - Chord $ PQ $ equals 7 units. - Chord $ RQ $ equals 7 units. - Chord $ TS $ equals 11 units.4. **Diagram Description**: - A circle with center $ C $. - The measure of $ \angle DEF $ is $ 65^\circ $. - The measure of $ \angle DFC $ is a right angle. - Chord $ DE $ equals $ x $ units.5. **Diagram Description**: - A circle with two intersecting chords $ PQ $ and $ RS $. - Chord $ PR $ equals $ 9x - 3 $. - Chord $ QS $ equals $ 7x + 5 $.#### Exercise 6: Determine whether $ AB $ is a diameter of each circle. Explain your reasoning using a theorem.**Diagrams:**a. **Diagram Description**: - A circle with a line segment $ AB $. - Chords $ AM $ and $ BN $ each measure 17 units. - $ \angle M $ is a right angle.b. **Diagram Description**: - A circle with a line segment $ AB $. - Chords $ AM $ and $ BN $ each measure 6 units. - $ \angle M $ measures $ 103^\circ $.

Answered: In Exercises 1 and 2, use the diagram…

Math

Geometry

In Exercises 1 and 2, use the diagram of OT. 1. If mPQ = 130°, find mRQ. 2. If mPR = 100°, find mPQ. 7. R

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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Question

Please do #1.

### Educational Exercise on Circle Geometry

#### In Exercises 1 and 2, use the diagram of ∠OT.

1. **Given**: $ m\angle PQ = 130^\circ $
- **Find**: $ m\angle RQ $

2. **Given**: $ m\angle PR = 100^\circ $
- **Find**: $ m\angle PQ $

#### In Exercises 3–5, find the value of $ x $. Show your work on #5.

3. **Diagram Description**:
- A circle with center $ T $.
- Chord $ PQ $ equals 7 units.
- Chord $ RQ $ equals 7 units.
- Chord $ TS $ equals 11 units.

4. **Diagram Description**:
- A circle with center $ C $.
- The measure of $ \angle DEF $ is $ 65^\circ $.
- The measure of $ \angle DFC $ is a right angle.
- Chord $ DE $ equals $ x $ units.

5. **Diagram Description**:
- A circle with two intersecting chords $ PQ $ and $ RS $.
- Chord $ PR $ equals $ 9x - 3 $.
- Chord $ QS $ equals $ 7x + 5 $.

#### Exercise 6: Determine whether $ AB $ is a diameter of each circle. Explain your reasoning using a theorem.

**Diagrams:**

a. **Diagram Description**:
- A circle with a line segment $ AB $.
- Chords $ AM $ and $ BN $ each measure 17 units.
- $ \angle M $ is a right angle.

b. **Diagram Description**:
- A circle with a line segment $ AB $.
- Chords $ AM $ and $ BN $ each measure 6 units.
- $ \angle M $ measures $ 103^\circ $.

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