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In the figure, if FR=FG, the measure of arc FG is 130, and measure of arc FQ is 28, then what is RPG, in degrees?

 Apr 28, 2020
edited by Guest  Apr 28, 2020
 #1
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Where is the referred to figure ?  cheeky

 Apr 28, 2020
 #2
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here's the diagram

 Apr 28, 2020
 #3
avatar+659 
+2

1. Connect RG

2. Since FR=FG, triangle FRG is isosceles with F as the vertex.

3. Angle GRF subtends arc GF, which is 130, therefore angle GRF = 130/2 = 65

4. Since FRG is isosceles, that means FRG=RGF.

 

5. Angle GFR = 50 because all triangles have an angle sum of 180, and we know that two angles are 65 degrees. (180 - 65 * 2)

6. Angle PGF subtends arc FQ, so angle PGF = 28/2 = 14

7. Conside triangle PFG, we know the measure of two angles GFR and PGF is  50 and 14, respectively. That means the third angle GPF is 180 - 50 - 14 = 116

8. By supplements angle RPG=180116=64

 

Done

 Apr 29, 2020

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