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# If angle B = 39 degrees and arc PS = 116 degrees, find the degree measure of arc AS. Picture: https://latex.artofproblemsolving.com/1/4/0/1

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So, I am trying to solve this problem but it is quite weird. I start out with labeling that angle B is 39 degrees and arc PS is 116 degrees. I am not to sure what is the relationship between angle B and arc AP. All I know is that the arc AP and triangle BAP share segment AP. That means that the measure of arc AP is twice the measure of angle B which is 78. To find arc AS we subtract 360-78-116 which equals 166. But 166 is not the answer. I know that arc AP is probably not twice angle B. How do you solve this problem? Also, if you are going to refer me to this page: https://web2.0calc.com/questions/pls-help-due-tmrow_7 then I am going to tell you that CPhill got the wrong answer. PLEASE HELP!

Feb 26, 2020

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I just  made  a  typo in the original problem....I used  38  instead of 39.....here is the  corrected  answer  :

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If angle B = 39 degrees and arc PS = 116 degrees, find the degree measure of arc AS.

Angle B =  (1/2) ( arc AS - arc AP)

39  =  (1/2) (arc AS - arc AP)

78  =  arc AS - arc AP     (1)

And

arc AS + arc AP  + arc PS  = 360

arc AS + arc AP   +  116  =  360

arc AS  + arc AP  =  244   (2)

arc AS - arc AP   =  78

arc AS +  arc AP  = 244

2 arc AS  =  322      divide by 2

arc AS  =  161°

Feb 26, 2020