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R Example 6: Find the following values for OS. PK is a diameter. 1. mPR = 2. mРМ %3D 80° W 40° 65° 3. mRWM = 4. тPK - 5. MRPM = 6. MPMR =

R Example 6: Find the following values for OS. PK is a diameter. 1. mPR = 2. mРМ %3D 80° W 40° 65° 3. mRWM = 4. тPK - 5. MRPM = 6. MPMR =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 9E
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**Example 6:** Find the following values for circle \( \bigodot S \). \( \overline{PK} \) is a diameter. 1. \( m\overset{\frown}{PR} = \) 2. \( m\overset{\frown}{PM} = \) 3. \( m\overset{\frown}{RWM} = \) 4. \( m\overset{\frown}{PK} = \) 5. \( m\overset{\frown}{RPM} = \) 6. \( m\overset{\frown}{PMR} = \) ### Diagram Explanation: The diagram shown is a circle with center \( S \). The circle has several points labeled around it: \( P, R, W, K, \) and \( M \). - \( \overline{PK} \) is indicated as the diameter of the circle. - The angle \( \angle RSW \) is marked as \( 80^\circ \). - The angle \( \angle WSK \) is marked as \( 40^\circ \). - The angle \( \angle MSP \) is marked as \( 65^\circ \). These angles are central angles, meaning they span from the center of the circle \( S \) to the circumference at points \( R, W, K, \) and \( M \). Use this information to find the arcs or measures around the circle associated with these angles, considering that the measure of an arc is equivalent to the measure of its central angle in degrees.
Transcribed Image Text:**Example 6:** Find the following values for circle \( \bigodot S \). \( \overline{PK} \) is a diameter. 1. \( m\overset{\frown}{PR} = \) 2. \( m\overset{\frown}{PM} = \) 3. \( m\overset{\frown}{RWM} = \) 4. \( m\overset{\frown}{PK} = \) 5. \( m\overset{\frown}{RPM} = \) 6. \( m\overset{\frown}{PMR} = \) ### Diagram Explanation: The diagram shown is a circle with center \( S \). The circle has several points labeled around it: \( P, R, W, K, \) and \( M \). - \( \overline{PK} \) is indicated as the diameter of the circle. - The angle \( \angle RSW \) is marked as \( 80^\circ \). - The angle \( \angle WSK \) is marked as \( 40^\circ \). - The angle \( \angle MSP \) is marked as \( 65^\circ \). These angles are central angles, meaning they span from the center of the circle \( S \) to the circumference at points \( R, W, K, \) and \( M \). Use this information to find the arcs or measures around the circle associated with these angles, considering that the measure of an arc is equivalent to the measure of its central angle in degrees.
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