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In the figure, if \(FR = FG\), the measure of arc \(FG\) is \(130^\circ\), and measure of arc \(FQ\) is \(28^\circ\), then what is \(\angle RPG\), in degrees?

 

 Jan 22, 2021
 #1
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Angle RPG = (130 + 28)/2 = 79 degrees.

 Jan 22, 2021
 #2
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Arc RG = 100º      ∠GFR = 1/2 * 100 = 50º

 

Arc FQ = 28º         ∠FGQ = 1/2 * 28 = 14º

 

∠FPG = 180 - (50 + 14) = 116º

 

∠RPG = 180 - ∠FPG = 64º

or

∠RPG = (arc GR + arc FQ) / 2 

 

∠RPG = (100º + 28º) / 2 = 64º

 Jan 22, 2021
edited by jugoslav  Jan 22, 2021
edited by jugoslav  Jan 22, 2021
 #3
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thank you so much! :))

Guest Jan 22, 2021

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