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In the figure, point A is the center of the circle, the measure of angle RAS  is 74 degrees, and the measure of angle RTB is 23 degrees. What is the measure of minor arc BR, in degrees?

 

 Nov 13, 2020
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Connect RA  and  SA

 

Note that since  RA  = SA   (they are both radii)  then triangle RAS  is isosceles

 

So  angle  SRA = angle TRA=    [ 180  - angle RAS  ]  / 2 =    [ 180 -74 ]  / 2  =   90 - 37  =  53°

 

And angle RTB = angle RTA

 

And considering  triangle RAT,   by the exterior angle theorem,  angle    RAB =  angle TRA  +  angle RTA 

 

Angle RAB = 53  + 23  =  76°

 

But angle  RAB  is a central angle  equaling the measure of  minor arc BR  =  76°

 

 

cool cool cool

 Nov 13, 2020

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