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

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
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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### 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 \( 103^\circ \).
Transcribed Image Text:### 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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