Given circle A to the right, FI is a diameter, CB || GH and GH || FI. If arc CB = 60º and arc CH ≅ arc GF, what is the measure of arc BG?
a. 30º
b. 45º
c. 72º
d. 24º
+51 Arc IF is 180 degrees. Since arc CH and GF are congruent, arcs CH, BG, HI, and GF are all congruent, as this is in a circle. 180 degrees - 60 degrees = 120 degrees = CH + BG + HI + GF. Since they are all congruent, we can say that all of the arcs equal BG, so 120 degrees = 4BG, so 30 degrees = BG. The answer is a.
+51 Arc IF is 180 degrees. Since arc CH and GF are congruent, arcs CH, BG, HI, and GF are all congruent, as this is in a circle. 180 degrees - 60 degrees = 120 degrees = CH + BG + HI + GF. Since they are all congruent, we can say that all of the arcs equal BG, so 120 degrees = 4BG, so 30 degrees = BG. The answer is a.
