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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

 

 May 11, 2020

Best Answer 

 #1
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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. 

 May 11, 2020
 #1
avatar+51 
+1
Best Answer

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. 

trumpstinks May 11, 2020

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