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?
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=180−116=64
Done