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In the figure, point \(O\) is the center of the circle, the measure of angle \(RTB\) is 28 degrees, and the measure of angle \(ROB\)  is three times the measure of angle \(SOT\). What is the measure of minor arc \(RS\), in degrees?

 

 

tertre  Mar 30, 2018
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2+0 Answers

 #1
avatar+85673 
+2

 

 

Since ROB  and SOT  are central angles....their measures = the measures of their intercepted arcs

 

So....We have  that

 

m RTB  =  (1/2) ( m ROB  - m SOT)

 

28°  = (1/2) ( 3m SOT - m SOT)   multiply both sides by 2

 

56°  =  2mSOT       divide both sides by 2     

 

28°  = mSOT

 

So....mROB  =  3 * 28   =  84°

 

So  RS  =  180 -  28  -   84   =   68°

 

 

 

cool cool cool

CPhill  Mar 30, 2018
 #2
avatar+2269 
+1

Thanks so much, CPhill!

tertre  Mar 30, 2018

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