We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+2
358
2
avatar+4223 

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?

 

 

 Mar 30, 2018
 #1
avatar+100571 
+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

 Mar 30, 2018
 #2
avatar+4223 
+1

Thanks so much, CPhill!

tertre  Mar 30, 2018

13 Online Users

avatar