Given angle APS = 77 degrees and arc AP = 128 degrees, find the degree measure of arc PS.

ARC AS = 2 * 77

 

then PS =   360 - (2*77) - 128 = ..............^o

Let the center of a circle be O

 

∠AOP = 128º

 

∠APO = 1/2 (180 - 128) = 26º

 

∠SPO = 77 - 26 = 51º

 

arc PS = 180 - 2 * 51 = 78º